Vertical-Cavity Surface-Emitting Lasers for Medical Diagnosis

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Vertical-cavity surface-emitting lasers for medical diagnosis

Ansbæk, Thor; Yvind, Kresten; Chung, Il-Sug; Larsson, David

Publication date: 2012

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Citation (APA): Ansbæk, T., Yvind, K., Chung, I-S., & Larsson, D. (2012). Vertical-cavity surface-emitting lasers for medical diagnosis. Kgs. Lyngby: Technical University of Denmark (DTU).

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Vertical-cavity surface-emitting lasers for medical diagnosis PhD Dissertation

Submitted to the Department of Photonics Engineering at The Technical University of Denmark in partial fulﬁllment for the degree of Doctor of Philosophy

Thor Ansbæk 2012 Preface

This dissertation has been submitted to the Department of Photonics Engineer- ing at The Technical University of Denmark (DTU) for the partial fulfillment of the degree of Doctor of Philosophy (PhD). The main supervisor has been Associate Professor Kresten Yvind. I gratefully acknowledge the PhD Scholar- ship funded by DTU. Part of the thesis work has been funded by the NanoNose project and the support from the Danish Agency for Science and Technology’s Program Commision on Nanoscience Biotechnology and IT (NABIIT) is acknowledged. The motivation of the work has been to combine Vertical-Cavity Surface- Emitting Lasers with Micro-Opto-Electro-Mechanical Systems in order to ad- vance the field of Optical Coherence Tomography (OCT). It has been a highly motivating subject to work on and I would like to thank my main supervisor Kresten Yvind for giving me this opportunity and supporting my project in every manner. A cornerstone in the project has been the use of the novel High- index Contrast subwavelength Grating (HCG) and to this aim I would like to thank Il-Sug Chung for his supervision into this for me completely new field. Last but not least I would like to thank David Larsson for his supervision on the Volatile Organic Compound (VOC) sensor. The initial part of the PhD was spent on getting acquainted with Vertical- Cavity Surface-Emitting Laser (VCSEL) processing by the fabrication of bottom emitting VCSELs. Simultaneously, experiments where done coating an off-the- shelf VCSEL with polystyrene and measurering the response to Acetone vapour. I would like to thank Claus Højgård Nielsen for doing the plasma polymeriza- tion of the polystyrene coatings and Søren Dohn for giving me access to his environmetal chamber for performing the experiments. The second part of the PhD project has been spent on the fabrication of a tunable Fabry-Pérot filter with a HCG top mirror. I would like to thank Jong-Min Kim for his initial work on growing epitaxial wafers with InGaP and AlInP. In order to fabricate subwavelength gratings dry etching was a neccesity and I would like to acknowledge the efforts of Martin Schubert and Jin Liu on the GaAs dry etching using Reactive Ion Etching (RIE) and Inductively Coupled Plasma (ICP), respectively. The aim was to use the tunable filters as part of a Fourier Domain Mode-Locked (FDML) swept source and I would like to thank Sebastian Marschall for discussion on tunable filters for OCT and his help on setting up a swept laser for characterization of the filters. The main part of the characterization of the filters was done using a fiber-based transmission setup and I would like to thank Radu Malureanu for his help and guidance. The last year of the PhD has been a race to develop a tunable VCSEL. I would like to thank Elizaveta Semenova for shedding light on the art of epitax-

2 ial growth. I greatly appreaciated the help of Nadezda Kuznetsova and Sara Ek on the micro photoluminescene setup which was instrumental in measuring non-lasing VCSELs. Thanks go to Martin Schubert for setting up the characterization setup. Silvan Schmid is thankfully acknowledged for his help with laser Doppler vibrometer measurements on the mechanical properties of the VCSELs. Ole Hansen and Erik V. Thomsen are both thanked for their supervision on the Micro-Electro-Mechanical Systems (MEMS). Having been associated to DTU Fotonik and the adjacent DTU Nanotech for almost 7 years I have had the pleasure to work along a long list of friendly collegues and students. I have greatly appreciated the helpful environment. In particular I would like to thank Troels Suhr Skovgård, Sara Ek, Róz˙aShirazi and Andrei Andryieuski for the cheerfull atmosphere upheld in our oﬃce - plastered with cake pictures. Lastly I would like to thank my family for their support - in particular my girl friend Benedicte Ersted Jensen who has supported me all the way and made sure that life went on as usual outside the world of research. This thesis is dedicated to my grandmother Jutta Ursula Elisabeth Chris- tensen.

Thor Ansbæk

September 30, 2012

Supervisors: Kresten Yvind Il-Sug Chung David Larsson Department of Photonics Engineering Technical University of Denmark Ørsted Plads 344 2800 Kgs. Lyngby Abstract

This thesis deals with the design and fabrication of tunable Vertical-Cavity Surface-Emitting Lasers (VCSELs). The focus has been the application of tunable VCSELs in medical diagnostics, specifically OCT. VCSELs are candidates as light sources for swept-source OCT where their high sweep rate, wide sweep range and high degree of coherence enable deep probing of tissue at acquisition rates that will eliminate the effects of rapid involuntary eye movements. The main achievement of the dissertation work has been the development of an electro-statically tunable VCSEL at 1060 nm with wide tuning range and high tuning rate. The VCSEL is highly single-mode and inherently polarization stable due to the use of a High-index Contrast subwavelength Grating (HCG). HCG VCSELs are presented with 1.5% relative tuning range at a tuning rate of 850 kHz. The thesis reports on the analysis of narrow linewidth Fabry-Pérot filters with dissimilar mirrors and the design of such Fabry-Pérot cavities for VCSELs. Fabrication of InGaAs multiple quantum wells with GaAsP strain balancing layers is covered together with the growth and wet chemical etching of InAlP. The fabrication of the proposed Fabry-Pérot filters and VCSELs is outlined and the results on their characterization reported.

4 Danish Resumé

Denne afhandling omhandler design og fremstilling af overfladeemitterende vertikal kavitets lasere med variabel resonansbølgelængde. Disse lasere udvikles med henblik på brug indenfor medicinsk diagnostik, nærmere bestemt optisk kohærens tomografi. Denne type laser er oplagt som lyskilde til optisk ko- hærens tomografi hvor den høje repetitionsrate, brede bølgelængde tunbarhed og høje grad af kohærens muliggør dybdeafbildning af øjets lagstruktur uden tab af opløsning på grund af ufrivillige øjenbevægelser. Hovedresultatet i afhandlingen er udviklingen af en overfladeemitterende vertikal kavitets laser ved 1060 nm hvor bølgelængden ændres hurtigt i et bredt om- råde ved elektro-statisk kraft. Denne type laser udmærker sig endvidere ved at være monokromatisk og lineært polariseret. Denne polariseringsbestemthed er opnået ved brug af et optisk gitter med en periode mindre end lysets bølgelængde og et brydningsindeks meget højere end det omgivende materiale (luft). Med denne type laser demonstreres en relativ bølgelængdeændring på 1.5% af cen- terbølgelængden ved en repetitionsrate på 850 kHz. I afhandlingen gennemgås teorien for et Fabry-Pérot optisk filter med smal optisk båndbredde hvor filterets to spejle er af forskellig type. Teorien for et Fabry-Pérot filter udvides til at gælde for overfladeemitterende lasere og de relevante designovervejelser for lasere, der kan dække et bredt spektralt om- råde, gennemgås. Afhandlingens andet store resultat er udviklingen af frem- stillingsprocessen til at lave disse Fabry-Pérot filtre og lasere med InGaAs kvan- tebrønde under tøjning. For at kunne danne et tomrum som muliggør ændring af bølgelængden ved elektro-statisk kraft er offeræts af InAlP undersøgt. På baggrund af de valgte designs fremstilles Fabry-Pérot optiske filtre og overfladeemitterende vertikal kavitets lasere, og deres elektro-optiske egenskaber undersøges eksperimentelt.

5 Contents

1 Introduction 9 1.1 Optical coherence tomography ...... 9 1.2 Tunable semiconductor lasers ...... 11 1.3 Stateoftheart ...... 13 1.4 Thesisoutline...... 15

2 Theory and design 17 2.1 Fabry-Pérotetalon ...... 17 2.2 Mirrors ...... 18 2.2.1 Method ...... 19 2.2.2 HCG...... 20 2.3 Fabry-Pérot ﬁlter ...... 24 2.3.1 Resonance wavelength ...... 24 2.3.2 Transmission ...... 26 2.4 HCG-VCSEL ...... 29 2.4.1 Lasingcondition ...... 31 2.4.2 Method ...... 32 2.4.3 Two mirror Fabry-Pérot cavity ...... 32 2.4.4 Three mirror Fabry-Pérot cavity ...... 36 2.4.5 Summary ...... 38 2.5 Electro-static actuation ...... 40 2.5.1 Static operation ...... 40 2.5.2 Dynamic operation ...... 42

3 Device fabrication 46 3.1 Epitaxialgrowth ...... 46 3.1.1 InGaAsMQW ...... 48 3.1.2 VCSEL ...... 50 3.1.3 InAlP ...... 51 3.2 Sacrificial release etch ...... 53 3.2.1 General considerations ...... 53 3.2.2 InAlP sacrificial etch ...... 54 3.2.3 Results ...... 55 3.3 Grating pattern transfer ...... 56 3.3.1 Si3N4 mask...... 57 3.3.2 ZEPmask...... 58 3.3.3 HSQmask ...... 59 3.4 HCG Fabry-Pérot filter ...... 60

6 3.5 VCSEL processing ...... 60 3.6 HCG-VCSEL processing ...... 61 3.7 Summary ...... 62

4 Fabry-Pérot ﬁlter results 63 4.1 Transmission measurements ...... 63 4.1.1 Fiber-based setup ...... 63 4.1.2 Filter transmission ...... 64 4.2 Discussion...... 65

5 VCSEL results 66 5.1 Experimentalsetup...... 66 5.2 VCSEL ...... 67 5.2.1 Device structure ...... 67 5.2.2 Laser characterization ...... 67 5.2.3 Discussion...... 70 5.3 HCGVCSEL ...... 71 5.3.1 Device structure ...... 71 5.3.2 Laser characterization ...... 72 5.3.3 Static wavelength tuning ...... 73 5.3.4 Swept wavelength tuning ...... 74 5.3.5 Mechanical characterization ...... 75 5.3.6 Discussion...... 77

6 Conclusion 78

A Fabry-Pérot Interferometer 80

Acronyms 82

List of publications 85

Bibliography 86

Chapter 1

Introduction

In this chapter an introduction to the ﬁeld of research and the motivating application is given. A popular account of Optical Coherence Tomography (OCT) and the use of swept sources is given in Sec. 1.1 to motivate the work. Here it is described why semiconductor lasers are interesting for swept source OCT. This is followed up in Sec. 1.2 by a short review on methods for making semiconductor based tunable lasers. We focus on a particular type of semiconductor laser, namely the VCSEL, which we argue is a good candidate light source for swept- source OCT systems. The state-of-the-art in tunable VCSELs is discussed in Sec. 1.3. The chapter ends with an outline of the thesis, covered in Sec. 1.4.

1.1 Optical coherence tomography

Light sources, covering parts of the electromagnetic spectrum, are used exten- sively to determine how light is reflected or absorbed by matter. Spectroscopy finds its application in various fields such as medical diagnostics, environmental sensing and material inspection. The requirements on such light sources vary widely depending on the application. In Optical Coherence Tomography (OCT) there is an expressed need for fast tunable lasers that can speed up the image acquisition rate, providing the physician with a real-time diagnostic tool. The focus of this thesis has been to investigate whether a monolithic semiconductor optical filter can provide a rapidly tunable light source covering a wide wavelength range usefull for OCT1. The analysis of cross-sectional images of tissue is an important diagnostic tool within medicine. These cross-section images, or slices, show the cellular structure of the tissue and are in particular used in the diagnostics of malignant tissue. There are two distinct methods to obtains such a slice. The traditional method is by taking a biopsy2, which is an invasive procedure also known as histology. In many areas non-invasive techniques are preferred and the use of penetrating waves for this purpose is referred to as tomography. Imaging modalities range from tomography using x-rays and visible light to ultrasound. OCT is a technique by which a depth-resolved image of the tissue is acquired

1Rapidly refers to > 100 kHz sweep rate and widely to > 50 nm. 2In a biopsy a small amount of tissue is removed from the patient. This is then sliced, stained (colored) and inspected by microscopy.

9 CHAPTER 1. INTRODUCTION with micrometer resolution using near-infrared light. This is particularly usefull in the diagnoses of eye diseases where the diagnostic tool must be non-invasive. The depth-resolved image is acquired by sampling the interference between two identical light beams - one reflected by a mirror, the other reflected from the tissue - in a Michelson-type interferometer. By varying the phase delay of one arm, the reflections at different depths in the tissue for which the phase delay matches can be measured. In OCT the light source must emit within the optical window (also referred to as the therapeutic window) which is the wavelength range within which the light has the largest penetration depth. There are two major absorbing components of tissue that determine the optical window. These are hemoglobin (red blood cells, Hb) and water. Fig. 1.1 shows the absorbance of these two components together with the absorption of melanin in the retina and skin. The eye mainly consist of water, or more precisely vitreous humor, which the light must propagate through to reach the retina. Above 1300 nm light is mainly aborbed by water, while below 650 nm oxygenated and deoxygenated hemoglobin (HbO2/Hb) absorbs the light. Hence OCT is mainly done in the wavelength range of 600-1300 nm with the current standard being 850 nm for ophthalmology and 1300 nm for dermatol- ogy. This makes direct bandgap semiconductor materials from the group III and V of the periodic table a good choice as light source. In particular III-V light sources made from AlInGaAs grown on GaAs-substrates will be able to cover the full range from 850-1300 nm. Currently the dominant technology is Spectral-Domain OCT (SD-OCT) where super-luminescent diodes are used as light sources together with grating-based spectrometers for obtaining the resulting interference scan in the Fourier domain. Depending on the wavelength either complementary metal-oxide-semiconductor (CMOS) or InGaAs line scan sensors can be used with scan rates of 142 kHz and 91 kHz, respectively3. Within the OCT research community there is a technology push towards Swept Source OCT (SS-OCT) where a tunable light source is used together with a pho- todetector. It is believed that SS-OCT will improve imaging depth and speed, enabling both the anterior and retina to be imaged at video-rate in one instru- ment with reduced motion artifacts [1, 2, 3]. Tunable semiconductor lasers have been attracting increasing attention within the field of OCT where they hold the promise of 3D eye scans acquisition on a time scale that will make motion artifacts negligible.

3The values are for the top-end models from http://www.baslerweb.com/Basler (CMOS) and http://www.goodrich.com/GoodrichGoodrich (InGaAs).

10 CHAPTER 1. INTRODUCTION

10 ] -1

10 [cm a

HbO

-1

W ater

10 Extinctioncoefficient,

Retina

Skin

-2

500 1000 1500 2000 2500

W avelength [nm]

Figure 1.1: Extinction coeﬃcient of typical tissue constituents encountered in OCT. The white region is referred to as the optical window since it is the optimum trade-oﬀ between water and blood absorption (courtesy of http://omlc.ogi.edu/spectra/).

1.2 Tunable semiconductor lasers

The laser started out as a technology without a clear-cut application, but has become ubiquitous with applications ranging from surgery to DVD players. Semi- conductor diode lasers offer a well-established mass-production platform as well as great diversity in wavelength span and functionality. One prominent functionality is wavelength tunability, which allows dynamic control of the emission wavelength. In 1917 Albert Einstein introduced the concept of spontaneous and stimulated emission of radiation with energy E E , from a molecule going from m − n an higher energy state Em to a lower energy state En[4]. However it was not until 40 years later when Charles H. Townes et al. published their article on the theory of the Microwave Amplification by Stimulated Emission of Radia- tion (maser), with the idea of applying feedback to the amplifcation of radiation, that the the field took off [5]. Simultaneously with Townes, Gordon Gould had sketched his ideas on the Light Amplification by Stimulated Emission of Radi- ation (laser) in his laboratory notebook [6]. Gordon Gould recognized that a Fabry-Pérot interferometer could be used to provide the feedback of the stimulated emission required for lasing. Shortly thereafter, the semiconductor diode laser was demonstrated for both GaAs and GaAsP semiconductor diodes [7, 8]. The present work relates directly to this effort - with the research field having moved to more advanced electro-optical design made possible by continuing im- provements in fabrication technology. With the advent of broadband internet

11 CHAPTER 1. INTRODUCTION and semiconductor lasers during the late 90’s there has been a great deal of both commercial and scientific interest in advancing the field of telecommunication. Optical fibers based on silicon oxide have largely replaced traditional copper wires as they enable longer transmission distances and transmission of multiple signals by Wavelength Division Multiplexing (WDM). Using wavelength multiplexing the electronic data are encoded at different wavelengths all carried by a single fiber. This provides a straight-forward route of expanding the capacity of fiber optic networks. Instead of needing one laser assigned to each wavelength, a significant cost advantage and flexibility could be achieved by using a tunable laser that could dynamically address different wavelengths. A great deal of commercial effort was put into developing such light sources in the years preceeding the dot-com bubble in 2000. The laser consists of an optical gain medium with feedback provided by an optical resonator. The optical resonator, known as the Fabry-Pérot interferometer, consists of two opposing mirrors. The cavity mode for such an interferometer is given by [9] 2nL λ = ,m N∗ (1.1) m m ∈ where m is the mode number, n the refractive index of the cavity and L the cavity length. The longitudinal lasing mode(s) are determined by Eq. (1.1) together with the gain and mirror reflectance spectrum. Lasing occurs at the modes for which the gain exceeds the mirror and cavity loss. From Eq. (1.1) it follows that tuning can be achieved by changing the refractive index of the cavity (n), the cavity length (L) or the lasing mode (m). The technological implementation of tunable semiconductor lasers mainly falls into three categories, namely the:

External Cavity Laser (ECL). • Edge-emitting Distributed Bragg Reflector (DBR) laser. • VCSEL. • Tunable external cavity lasers are widely used as implementation offer great flexibility, exploit the full gain spectrum of the Semiconductor Optical Ampli- fier (SOA) and can make use of multiple optical components for wavelength selective feedback. The majority of widely tunable ECLs are either of the Littrow, Littmann-Metcalf or Fabry-Pérot configuration. The advantage of the ECL is that high single-mode output powers can be achieved together with a wide tuning range, only limited by the gain medium [10]. In both the Littrow and Littman-Metcalf configuration a diffraction grating is used as the wavelength selective feedback to the SOA. The weak link in the Littrow and Littman- Metcalf configurations is the electro-mechanical tuning of the bulky diffraction grating and reflector, respectively. Miniaturization of the diffraction grating and reflector has been researched, but the tuning rate is still limited to kHz from size constraints [11, 12]. Using the fast angular rotation of polygon scan- ners to control the incident angle onto the grating in a Littrow configuration tuning rates up to 50 kHz have been shown [13, 14]. In the Fabry-Pérot configuration a Fabry-Pérot filter is used for wavelength selection, suppressing all other nearby wavelengths. Wide and rapid tuning can be achieved by Micro- Electro-Mechanical Systems (MEMS) Fabry-Pérot filters. Kuznetsov et al. have

12 CHAPTER 1. INTRODUCTION demonstrated 10% relative tuning at 100 kHz using the MEMS Fabry-Pérot filter as reflector [15]. Tunable edge-emitting DBR lasers were originally developed to target telecom- munications. For Sampled Grating DBR (SGDBR) wavelength tuning is achieved by tuning the reflection spectrum of the two cavity mirrors to coincide while tuning a phase section to match the propagation phase. Wide discontinuous wavelength tuning can be achieved with the added benefit that a SOA can be monolithically integrated to boost the power output. Recently DBR lasers have been proposed for SS-OCT by Insight Photonic Solutions which has achieved 100 nm tuning range at 200 kHz [16]. Fast Digital Signal Processing (DSP) are required in order to control the four electrodes of the laser diode that are controlling the wavelength tunability [17, 18]. The DSP must control the input currents according to a look-up-table that must be acquired by full calibration. Long-term drift in such devices is likely to lead to over-lapping wavelength scans and artifacts in OCT. Tunable VCSELs are favoured for commercial use due to the ability to con- duct wafer-level testing, which leads to significant cost-reduction during packaging. Tunable VCSELs will be reviewed in the following section. In the tunable VCSEL it is the Fabry-Pérot cavity length that is directly modulated. Due to their small size VCSELs allow tunability in the MHz range [19]. The power output is lower than tunable SGDBR lasers and ECLs for electrically pumped versions. Praevium Research has demonstrated a tunable optically pumped VCSEL with 100 nm tuning range at 1310 with tuning rates of 500 kHz [20]. While optically pumped VCSELs allows greater output power, their packaging is complicated by the requirement of an external laser diode. Widely tunable semiconductor lasers were originally developed for WDM systems in telecommunication, but recently focus has shifted toward other applications such as gas-sensing and medical imaging. In particular within SS-OCT there is an on-going race to establish tunable semiconductor lasers as the dominant technology. Emphasis has been put on external cavity lasers by companies such as Axsun, Santec, Exalos and Micron Optics - the best results showing 100 nm tuning range at hundreds of kHz. The competitors Thorlabs and In- sigth Photonic Solutions are focusing on optically pumped VCSELs and SGDBR lasers, respectively.

1.3 State of the art

Tunable VCSELs have been researched for more than two decades. The vertical- cavity optical design lends itself to a straight-forward implementation of mechanical tuning from a conceptual point of view. From Eq. (1.1) it follows that incorporating a variable air-gap as part of the cavity L the cavity-mode can be directly modulated. The idea to form a variable air-gap in a semicondutor device by sacrificial etching was already introduced in 1967 when Nathanson et al. presented the fabrication of resonant gate transistors [21]. In 1979 the first VCSEL was introduced by Ivars Melngailis and the research group of Kenichi Iga contin- ued to present the first Continous Wave (CW) operation at room temperature in 1989 with mW output power and 35 dB Side-Mode Suppression Ratio (SMSR) [22, 23, 24]. Less than a decade later, in 1995, the first electro-mechanically tunable VCSEL was introduced, demonstrating 10 nm tuning range [25]. The

13 CHAPTER 1. INTRODUCTION

∆λ Year QW λ0 λ0 SMSR Pmax f0 Type Ref. [nm] [%] [dB] [mW] [kHz] et al. 1997 InGaAs 980 1.2 30 0.150 300 E Vail [26] 1997 InGaAs 970 2.0 24 0.002 (500) E Sugihwo[27] 2004 AlGaInAs 1550 2.6 32 0.100 DC T Riemenschneider [32] 2007 GaAs 850 0.4 40 1.200 20 P Huang [33] 2008 AlGaAs 750 3.0 MM 0.012 700 E Cole [34] 2008 GaAs 850 0.4 45 2.000 3000 E Zhou [29] 2009 AlGaInAs 1550 2.6 60 3.500 350 E Yano [30] 2010 GaAs 850 2.2 40 0.170 DC E Davani[35] 2011 AlGaInAs 1550 5.6 45 3.500 DC T Gierl [28] 2011 AlGaInAs 1550 3.0 40 1.800 215 E Gierl [31]

Table 1.1: Summary of the research within tunable electrically-pumped VCSELs, λ0 is the center wavelength, Λλ is the dynamic bandwidth, SMSR is the single-mode suppresion ratio, Pmax is the maximum power and f0 the resonance frequency. Dif- ferent actuation methods have been used; E = electro-static actuation, T = thermal (bimorph) actuation and P = piezo-electric actuation. Further MM = multi-mode lasing and DC = direct-current modulation. tuning range was improved shortly after by a factor of two, achieving a 2% relative tuning range at kHz frequencies [26, 27]. In recent years even better results have been shown - approaching the limitation from the wide free-spectral range of VCSELs. Gierl et al. have demonstrated 6.6% relative tuning range at DC thermal large-signal tuning [28]. Zhou et al. have demonstrated MHz electro-static small-signal tuning with relative tuning ranges below 0.5% [29]. Currently the state-of-the-art within VCSELs, both rapidly and widely tunable, are hundreds of kHz with 3% relative tuning range at 1550 nm [30, 31]. Table 1.1 provides a summary of notable achievements of tunable VCSELs in chrono- logical order. Currently tunable VCSELs at 750, 850, 980 and 1550 nm have been presented covering the tuning schemes of electro-static, piezo-electric and thermal (bimorph) actuation. The fabrication of high-performance tunable VCSELs remains a challenge in the regard that both process development, cavity electro-optical design and the mechanical actuation must be optimized together. The best result to date have been presented by Gierl et al. who have used the optimized long-wavelength epitaxial structure of Amann et al. together with a micromachined electro- mechanical DBR top mirror to achieve 40 nm tuning range at 215 kHz [31]. The distinct advantage of the optical design of Gierl et al. is the highly stable single-mode plano-concave Fabry-Pérot cavity and high-index contrast DBRs. The high-index contrast DBRs provide the wide-band ultra-high reﬂectance (> 99.9%) needed for lasing. Promising result have also been shown by Huang et al. who have demonstrated MHz tuning rates by using a HCG top mirror. The distinct advantage of the optical design of Huang et al. is their use of the highly single-mode and polarization stable HCG. Through careful design and fabrication the HCG mirror provides wide-band ultra-high reﬂectance. Figure 1.2 shows a comparison between tunable VCSELs, ECLs and DBR laser diodes with regard to output power, tuning rate and range. The ECLs and DBR lasers outperform the VCSELs in terms of output power and tuning range. This is

14 CHAPTER 1. INTRODUCTION

VCSEL ECL DBR

6 This work/DTUThis

0.9 Insight

3.5

1.8 20 Exalos

5 UCBerkeley 10 15 15 Micron/Santec

12 Repetition[Hz] rate Yokogawa Axsun

1.2 Darmstadt/TUM 4

10 10

0 1 2 3 4 5 6 7 8 9 10

Relative tuning range, [%]

Figure 1.2: Bubble plot of the state-of-the art within tunable semiconductor lasers (VCSELs = red triangle, ECLs = green square, DBR = blue circle). The plot shows the mechanical resonance frequency versus the relative tuning range (the data label is maximum output power in mW). Data are taken from Tab. 1.1. at the expense of complicated packaging for the ECLs and the need for DSP for control of the DBR laser. VCSELs are currently unique in realizing MHz tuning rates. There is still room for signiﬁcant3.5 improvement in the relative tuning range and the power output can be boosted using SOAs.

1.4 Thesis outline

Tunable semiconductor lasers continue to be of research interest throughout the world due to their favorable cost-structure and high performance-to-size ratio. The focus of the thesis has been to make a widely and rapidly tunable electrically-pumped 1060 nm VCSEL. We have targeted > 50 nm tunability at MHz scan rates. Towards this aim ultra-high reflectivity mirrors have been fabricated in the form of DBRs and HCGs. Furthermore the epitaxial growth of optical gain material for the 1060 nm wavelength has been developed. Chapter 2 covers the analytical and numerical framework established for the design of Fabry-Pérot filters and VCSELs with HCG and DBR reflectors. Design rules for high finesse Fabry-Pérot filters are presented based on the application of an effective mirror model [36]. The influence of the mirror reflectance on the filter linewidth and transmission is discussed in the context of high finesse filters. Furthermore the optical cavity design of VCSELs is discussed with emphasis being put on how to increase the tuning efficiency of the VCSEL by reducing the

15 CHAPTER 1. INTRODUCTION cavity length and introducing an anti-reflective coating to the air-semiconductor interface to reduce the parasitic reflection. Lastly the electro-mechanical design of the suspended top mirror is discussed and the inherent trade-off in achieving both high scanning speed and wide wavelength tunability is presented. Both relate to the use of electro-static tuning. Chapter 3 goes through the process development that has been necessary to fabricate HCG VCSELs. The major contribution to the research field lies in the demonstration of a possible route to realize the monolithic integration of an anti-reflective coating into the epitaxial structure. To that aim the use of InAlP for sacrificial release has been investigated for the first time. Chap. 4 presents the results on a HCG Fabry-Pérot filter made in the GaAs material system. Chap. 5 shows the first demonstration of a VCSEL with an air-cladded HCG mirror substituted for the top p-DBR. The performance is presented in terms of the light-current-voltage characteristics and the optical spectrum.

16 Chapter 2

Theory and design

In this chapter the optical and electro-mechanical design of Fabry-Pérot filters and VCSELs is covered. The focus is on the Fabry-Pérot resonance effect, the threshold for lasing and the electro-static tuning of the cavity length. In Sec. 2.1 the key metric of the Fabry-Pérot etalon is briefly revisisted as this forms the basis for monochromaticity. In Sec. 2.2 the reflection properties of the High- index Contrast subwavelength Grating (HCG) is investigated. In Sec. 2.3 the design of Fabry-Pérot interferometers made up of dissimilar reflectors is analyzed and it is shown how a difference in reflectance is detrimental to the properties of the interferometer. Section 2.4 gives a walkthrough of the optical cavity design for VCSELs that have been fabricated with attention to achieving high tuning efficiency. Section 2.5 deals with the design of the Micro-Electro-Mechanical Systems (MEMS) for electro-static actuation.

2.1 Fabry-Pérot etalon

The Fabry-Pérot etalon is an example of an optical resonator. The etalon is a plate of ﬁxed thickness L with index of refraction n (the surrounding medium has index of refraction n0). For a normal incidence beam of light the transmission spectrum has a maximum at the wavelength [9]

2nL λ = ,m N∗ (2.1) m m ∈ with a finesse FSR π√R = = (2.2) F FWHM 1 R − where R is the power reflectance of the two mirrors making up the optical resonator. The finesse is the ratio of distance to the neighbouring peaks, the Free Spectral Range (FSR), to the Full-Width at Half-Maximum (FWHM). Hence the higher the finesse, the better the Fabry-Pérot etalon is at picking out a particular wavelength. The distance between each peak, the FSR, can be derived to be 2 λm ∆λ = λm λm+1 = (2.3) − 2Lng

17 CHAPTER 2. THEORY AND DESIGN

where ng is the group index

1 1 1 λ ∂n − = 1 m (2.4) n n − n ∂λ g m The group index can be taken to be n when the wavelength dependence of the refractive index is negligible. An example of an etalon is a GaAs wafer. For a 350 µm thick GaAs etalon the FSR is 0.45 nm at λ = 1060 nm. The field reflection coefficient at the semiconductor-air interface will be n n 3.5 1 r = 2 − 1 = − = 0.55 (2.5) n2 + n1 3.5 + 1 and hence the power reflectance will be 31%. This is enough that modulation in the transmission spectrum can show up, which is commonly referred to as Fabry-Pérot fringes. The finesse of such a cavity is only 2.5 which means that the FWHM is comparable to the FSR. The two reflecting surfaces of the etalon can also be exchanged with two highly reflecting mirrors. The resulting Fabry-Pérot interferometer can be made tunable by changing the distance between the two mirrors. The focus here will be on monolithic vertical-cavity Fabry-Pérot interferometers. For an electro- statically tunable interferometer to require reasonable tuning voltage and at the same time have a very high mechanical resonance-frequency the cavity length must be small. For a λ/2-cavity the FSR will be the same as the interferometer wavelength and thus a high finesse is required to have a narrow FWHM. It follows from Eq. (2.2) that the mirrors must have an ultra-high reflectance, R.

2.2 Mirrors

The high finesse Fabry-Pérot filter and the VCSEL have in common the requirement of high reflectance mirrors. Metal mirrors can provide very high reflectance on the order of 98-99 % over a broad range. In fact the first demonstrations of the VCSEL was made using Au reflectors [22, 23]. High reflectance mirrors can also be fashioned by depositing a number N of λ0 / λ0 thin film pairs of 4nL 4nH different low and high refractive index nL and nH . DBRs are an embodiment of such high reflectance mirrors and are either deposited dielectric mirrors or epitaxially grown semiconductor mirrors. For the first demonstration of room- temperature lasing of a VCSEL a 5-pair SiO2/TiO2 stack was used as the output mirror, having a reflectance maximum of 99.2%. It was early recognized that a very high reflectance, as well as large gain to cavity length ratio, was necessary in order to reduce the threshold current [37]. The AlGaAs/GaAs mirror pair has proven an ideal high-reflectance mirror for VCSELs. The lattice-matching of AlGaAs to GaAs enables very thick atomically abrupt layers to be grown making high quality mirrors of reflectance above 99.5%. Increasing the number of mirror pairs beyond 25 99.9 % reflectivity is routinely obtained only limited by free-carrier absorption. An advantage of the AlGaAs/GaAs DBR is that the reflectivity is easily scalable and that the stopband is well-behaved. Recently a new class of broadband ultra-high reflectance mirrors has been

18 CHAPTER 2. THEORY AND DESIGN demonstrated, the HCG [38]. These results expand on the narrowband ultra- high reflectance grating mirrors that was presented under the term of Guided- Mode Resonance (GMR) [39]. Another embodiment of essentially the same structure, the GIant Reflectivity to zero Order (GIRO) grating, was shown to have broadband high-reflectivity[40, 41, 42]. Figure 2.2 shows the reflectance of both a DBR and HCG mirror.

L w

tHCG nH

substrate

Figure 2.1: Schematic drawing of the HCG with grating period Λ, thickness tHCG and w duty cycle DC = Λ given by the width, w of the high refractive index, nHCG, medium. The high refractive index region is surrounded by air and space the length g above the substrate.

2.2.1 Method In order to design the mirrors a method to calculate their reflectance, in terms of geometrical and physical properties, is needed. The reflectance of a multi-layer film such as the DBR is conveniently calculated using the Transmission Matrix Method (TMM). For reflectance at normal in- 1 cidence the electric field and magnetic flux density at the input plane (E1 and B1) and output plane (E2 and B2) of a thin film can be expressed as

E cos(δ/2) i sin(δ/2) E 1 = n√ǫ0µ0 2 (2.6) B1 in ǫ µ sin(δ/2) cos(δ/2) B2 " √ 0 0 #

M12 where n is the thin film| refractive index{z and δ the phase} difference between a round-trip of the thin film 4πnt δ = (2.7) λ having a thickness t[43]. For a multi-layer film the transmission matrix of each layer is then multiplied to get the transmission matrix for the full stack.

1Since there is not magnetic media the magnetic ﬂux density is related to the magnetic ﬁeld by the magnetic permeability in vacuum

19 CHAPTER 2. THEORY AND DESIGN

The reflectance of a subwavelength grating, such as the HCG, is calculated using Rigorously Coupled Wave Analysis (RCWA)[44]. This method enables the computation of the transmittance and reflectance of a thin film with a periodic refractive index modulation. The HCG is an example of an ideal binary modulation. The periodic refractive index modulation of the grating and the resulting periodic modulation of the electric and magnetic field is presented through a Fourier series of order N. Applying Maxwell’s equations and boundary conditions to the electric and magnetic fields inside and outside the grating, a system of coupled equations results. Here the implementation of RCWA named RODIS has been used for the calculation of the HCG reflectance [45]. Convergence analysis using RODIS for calculating the reflectance of a HCG shows that N 30 4 ≥ to achieve an error in the reflectance lower than 5 10− . A thorough analytical treatment of the HCG shows that the ultra-high× reflectance comes from the suppression of higher order diffraction modes and the cancellation of the two first modes [46].

2.2.2 HCG The HCG enables ultra-high reflectivities > 99.9% by surrounding a sub-micron thick, high-refractive index material grating layer with a low-refractive index material [19, 38]. The use of broadband HCGs has so far been limited to coupled cavity design where it has been used to increase the reflection of a low-Q cavity consisting of 2-4 pairs of top DBRs and 34 pairs of bottom DBRs [47, 48]. The only demonstration of a VCSEL with a HCG as top reflector has been done at 1330 nm using a Si/SiO2 HCG with 9 mA threshold current at 15◦C [49]. The HCG only requires a single high-refractive index layer surrounded by low-refractive index material. This makes it markedly easier to fabricate than a similar approach to DBRs of increasing the refractive index contrast which requires several layers of dissimilar materials [50, 51, 52]. While the DBR requires the control of only two parameters, the optical thicknesses of the two layers, the HCG requires the control of three parameters, the grating thickness tHCG, the period P and duty cycle Λ. From the carefull design of these parameters a photonic stopband similar to, or even exceeding, the high refractive index contrast DBR can be obtained. The HCG has the added advantage that when designed using grating bars (1D) strong polarization dependence can be achieved. Figure 2.2 shows the design employed throughout this thesis for λ0 = 1060 nm, which was calculated using RODIS. This HCG design shows broadband reflectivity for the TM mode, with the electric field perpendicular to the grating. This is an advantage when SOAs are to be used to boost the output power - with improper control of the polarization the power penalty can be up to 10 dB. In order to achieve very high HCG reflectance the grating period must be subwavelength in order to suppress all higher order diffraction modes other than the zeroth diffraction mode [46, 53]. This is because the ultra-high reflectivity effect depends on the destructive interference of the waveguide modes at the output plane of the HCG. The conditions for such cancellation in terms of the geometry can be found to be DC = 0.7 and tHCG = 300 nm and Λ = 500 nm for n = 3.21 [46]. Here all computations are done with n = 3.5. Figure 2.3 shows a 3D plot of the grating designs that yield an ultra-high reflectivity stopband of 40 nm around a center wavelength of λ0 = 1060 nm. In order to match the bottom DBR reflectance of the VCSEL with the top HCG we haven chosen a

20 CHAPTER 2. THEORY AND DESIGN

1 DBR 0.9 HCG TE HCG TM 0.8

0.7

0.6

0.5

Reflectance 0.4

0.3

0.2

0.1

0 900 1000 1100 1200 1300 1400 1500 Wavelength [nm]

Figure 2.2: Plot of the reﬂectance of a 35 pair Al0.9Ga0.1As/GaAs DBR (dotted) and HCG with DC = 0.72, Λ = 460 nm, tHCG = 280 nm and nHCG = 3.5. The reﬂectance for the HCG is plotted for both TE (dashed) and TM (solid) polarized light.

design with tHCG = 280 nm, DC = 0.72 and Λ = 460 nm. This particular design has a local reflectance minimum of 99.9% at λ0 = 1060 nm. The increasing reflectivity away from the center wavelength λ0 then compensates the decreasing reflectivity of the DBR which has a maximum reflection coefficient at λ0. Since the ultra-high reflectivity effect of the HCG depends on the destructive interference of two modes the grating thickness, and thus propagating phase, become a key parameter. Fig. 2.4 shows a contour plot of the GaAs HCG reflectance versus wavelength and grating thickness. From Fig. 2.4 it is seen that in order to achieve a broadband reflectivity of 99.5% or higher the grating thickness must be close to 275 nm. Epitaxial growth of GaAs enables precise control of the grating thickness, tHCG, to within 5 nm, and hence this is not out of reach. The period is well-controlled by e-beam± writing, while the duty cycle depends on the control of the e-beam exposure, development and pattern transfer. Figure 2.5 shows a contour plot of the GaAs HCG reflectivity at a wavelength of 1060 nm versus the grating thickness, tHCG, and the duty cycle DC. At a grating thickness of 280 nm the reflectivity stays above 99.5% for at duty cycle of 0.7-0.85. This corresponds to a difference in the grating bar width of 70 nm at the given grating period of 460 nm. Hence the HCG reflectance is not very sensitive to the grating duty cycle.

21 CHAPTER 2. THEORY AND DESIGN

λ = 1060 nm, ∆λ = 40 nm, R > 99.9% 0

320

310

300

290 Thickness [nm] Thickness

280

510 270 500 50 490 55 480 60 470 Duty Cycle65 [%] 460 70 450 75 440 80 430 420 Period [nm]

Figure 2.3: 3D plot of the combinations of grating thickness tHCG, duty cycle DC and grating period Λ required for a 40 nm photonic stopband with R > 99.9%. The refractive index of the grating is nHCG = 3.5.

However, the HCG reflectance is not the only parameter changing with the duty cycle, the HCG reflection phase θ will also change. For the DBR it is very convenient that the reflection phase is zero at the Bragg frequency, but the HCG reflection phase is generally non-zero at the design resonance wavelength which must be accounted for in the epitaxial design. Figure 2.6 shows a contour plot of the GaAs HCG phase versus grating thickness, tHCG, and duty cycle, DC.

22 CHAPTER 2. THEORY AND DESIGN

450

90 90 90 400 99 99 80

[nm] 350 99.5 70 90 Reflectance[%]

HCG 90 90 60 300 99.599 90 50 9999.5 99.599 99 250 9999.5 99.5 40 90

Grating Thickness,t 30 200 99.5 99 9999.5 90 20 150 99 90 10

900 950 1000 1050 1100 1150 1200 1250 Wavelength, λ [nm]

Figure 2.4: Contour plot of the HCG reﬂectance versus wavelength and grating thickness. The refractive index of the grating is nHCG = 3.5, duty cycle DC = 0.72 and period Λ = 460nm.

0.9 95 99 95 95 99.5 99 99 0.85 99.5 99.5 95

0.8 99.5 99 90 0.75 99.5 99 85 0.7 Reflectance[%] 99 99.5 80 0.65 95 99 0.6 95 Dutycycle,DC 75

0.55 95 95 95 70 0.5 99.599 99 9999.5 99.5 99 99.5 99.5 65 0.45 99 9999.5 95 95 0.4 60 260 265 270 275 280 285 290 295 300 Gratingthickness,t [nm] HCG

Figure 2.5: Contour plot of the HCG reﬂectance at λ0 = 1060 nm versus the grating thickness, tHCG, and duty cycle, DC.

23 CHAPTER 2. THEORY AND DESIGN

-60 0.9 -120 -45 -90 0.85 -60 100

-45 0.8 -30 -60

0.75 50 ] [ Relfectionphase, -30 -45 0.7 -15

0.65 0 -30

-15 q

0.6 HCG

Dutycycle,DC

0 o -15 0.55 -50 0 0.5 0 30 0.45 30 -100 30 60 0.4 260 265 270 275 280 285 290 295 300 Gratingthickness,t [nm] HCG

Figure 2.6: Contour plot of the HCG reﬂection phase θHCG at λ0 = 1060 nm versus the grating thickness, tHCG, and duty cycle, DC.

2.3 Fabry-Pérot ﬁlter

The two preceeding Secs 2.1 and 2.2 treated the Fabry-Pérot etalon and two types of reﬂectors, namely the DBR and HCG. Here we combine the two in what is the Fabry-Pérot interferometer seen in Fig. 2.7. Here the DBR is the bottom mirror, which is grown epitaxially on the substrate, and the HCG is the top mirror, which is patterned by surface micro-machining. From Eq. (2.1) we may conclude that the wavelength change is twice the change in gap distance for a interferometer with fundamental cavity m = 1, but the penetration depth of the mirrors will make the achievable wavelength change smaller.

2.3.1 Resonance wavelength

The mirrors of the cavity will be characterized by their reflection coefficient and reflection phase (which for the DBR is zero at the Bragg frequency). The reflection phase can be approximated to be linearly dependent on the wavelength and can hence be linearized around the center wavelength λ0 [36, 54, 55]

∂θ ∂λ 2πc 2πc θ(λ) = + θ(λ0) ∂λ ∂ω ω0 λ − λ0 2πc 2πc = τ + θ(λ ) − λ − λ 0 0 4πn L = g eﬀ + ϕ (2.8) − λ

24 CHAPTER 2. THEORY AND DESIGN

AlGaAs, nL GaAs, nH

Ei effectivereflectionplane

i(2βL1+ϕ) r1 = r1 e− HCGmirror | | L1

r1 Fabry-Perotcavity g r2 DBRmirror L2

z Et

Figure 2.7: Filter schematic (left) and model (right). The filter consist of a bottom distributed bragg reflector (DBR) and a top high-index-contrast subwavelength grating (HCG). In the model the mirrors are represented by hard mirrors with a reflectance |r|2 at a distance L and phase-shift ϕ from the physical reflection plane. where we have defined the reflection phase delay (∂θ/∂ω)

∂θ ∂λ ∂θ λ2 τ = 0 , (2.9) ≡ −∂λ ∂ω ω0 ∂λ λ0 × 2πc

penetration depth cτ Leﬀ vgτ = (2.10) ≡ 2ng and constant reﬂection phase delay 2πcτ 4πn ϕ + θ(λ0) = L + θ(λ0). (2.11) ≡ λ0 λ0 This allows us to rewrite the resonance condition as

4π(n0g + nL1 + nL2) λm = , (2.12) 2πm + ϕ1 + ϕ2 where n0 is the refractive index of the gap medium, g the gap distance and nL is the optical penetration depth of the mirrors of indices 1 and 2. The refractive index is that of the medium into which the light is reflected from the physical mirror. The effective mirror model provides the interpretation that the actual mirror can be replaced by a hard mirror at a distance Leff from the physical mirror position with a constant reflection phase that is independent of the wavelength, as illustrated in Fig 2.7. The tuning efficiency of the interferometer is ∂λ 4π m = . (2.13) ∂g 2πm + ϕ1 + ϕ2

For the HCG and DBR in Fig. 2.2 ϕ1 = 2.04π, ϕ2 = 6.69π, nL1 = 583 nm and nL2 = 1770 nm. Then the tuning eﬃciency as calculated for a fundamental mode cavity (m = 1) using Eq. (2.13) is 0.37.

25 CHAPTER 2. THEORY AND DESIGN

2.3.2 Transmission The transmission loss and the finesse are the most important parameters of a filter. The transmission is unity at theF filter resonance wavelength in the simple model of Eq. (2.12), but absorption loss and difference in the reflectance of the two mirrors will both result in reduced transmission. For application in WDM a finesse of > 200 is required, which corresponds to a FWHM of around 0.5 nm [56]. ForF application in OCT an even higher finesse of > 400 is required, which corresponds to a FWHM of around 0.15 nm at a centerF wavelength of 1060 nm. The transmission loss should be less than 3 dB. The transmission can be written (see App. A)

t 2 t 2 T = | 1| | 2| (2.14) FP (1 r r )2 + 4 r r sin2(δ /2) − | 1|| 2| | 1|| 2| ′ where t and r are the fresnel transmission and reflection coefficients, respectively, and δ′ the phase difference after a round-trip.

Loss-less The simplest case arise for the interferometer where there is no absorption loss, beam walk-off and the reflection phases are zero. With R = r1 r2 the filter transmission, using Eq. (2.14), becomes | || |

(1 R)2 T = − FP (1 R)2 + 4R sin2(δ/2) − 1 = (2.15) 1 + F sin2(δ/2) where F is referred to as the coefficient of finesse. From Eq. (2.15) the FWHM can be derived 1 T (δ ∆δ) = T (δ ) FP 0 ± 2 0 ⇒ λ2 1 ∆λFWHM = (2.16) 2πn0g √F The FWHM is an important parameter of the filter and is contained in the expression for the finesse, Eq. (2.2). From Eq. (2.16) it can be concluded that to decrease the filter linewidth the coefficient of finesse should be increased. In Fig. 2.8 the linewidth as calculated from Eq. (2.16) is plotted for different values of the reflectance R. A reflectance above 99.9% is required for the FWHM to be smaller than 0.1 nm for a λ-cavity.

Unequal reflectance In a typical bulk type etalon the reflectivity of the two mirrors will be the same. Equal mirror reflectance will be more difficult to achieve when the mirrors are of different types. To take into account the difference in reflectivity we can expand Eq. (2.14)

T T (1 r r )2 T = 1 2 1 2 (2.17) FP 2 2− | || | 2 (1 r1 r2 ) (1 r r ) + 4 r r sin (δ /2) − | || | − | 1|| 2| | 1|| 2| ′

26 CHAPTER 2. THEORY AND DESIGN

Finesse 124 156 208 313 627 Inf 10 1 0.2 λ/2 9 λ 0.9 3/2λ 0.1 8 2λ 0.8

7 0.7 0 0.999 0.9995 1 6 0.6

5 0.5

FWHM[nm] 4 0.4

3 0.3

2 0.2

1 0.1

0 0 0.975 0.98 0.985 0.99 0.995 1 Reflectance,R

Figure 2.8: Plot of the linewidth as function of the mirror reﬂectance for diﬀerent cavity lengths.

where the second fraction is the the same as Eq. (2.14) with R = r1 r2 and the first fraction is a pre-factor that determines the effect of the mismatch| || | of the two mirrors. This prefactor can be rewritten as (1 r 2)(1 r 2) T = − | 1| − | 2| (2.18) 12 (1 r r )2 − | 1|| 2| where we again assume the lossless case T = 1 R for both mirrors. This − function is one for r1 = r2 and for r1 = r2 it drops fast to zero. In case the two mirrors are not equal in their fabrication6 the resulting mirror reflectnace mismatch can induce a 5-10 dB transmission loss [50]. In the case of a 30- period Al0.9Ga0.1As/GaAs DBR with a reflectance of 99.97% the other mirror reflectance must be 99.91% to keep the loss below 3.1dB (corresponding to T 0.5). This means that the reflectance of the other mirror must be within 12 ≈ 600 ppm of the DBR reflectance. Figure 2.9 shows T12 in dB as a function of the reflectance, R = r r , for various values of the HCG reflection coefficient, | 1|| 2| r2. It can be seen that the higher the value of R, the smaller is the region within which the mirrors match to such a degree that the transmittance is above 50%. Lowering the total reflectance increases the window within which there is less than 3 dB loss, but it also decreases the linewidth as seen in Fig. 2.8. Hence there is a trade-off between lowering the tolerance on the mirror reflectance and narrow linewidth.

Absorption Loss The HCG and DBR mirrors are both doped to reduce the resistance and minimize the voltage drop across the substrate and the beam suspensions of the top

27 CHAPTER 2. THEORY AND DESIGN

3 dB specification

−5 Transmission [dB] −10

R = 0.9995 DBR R = 0.998 DBR R = 0.995 DBR −15 0.975 0.98 0.985 0.99 0.995 1 Reflectance R

Figure 2.9: Plot of the mismatch pre-factor T12 as a function of the Reflectance R = |r1||r2| for three different DBR Reflectances R2 = 99.5%, 99.8% and 99.95%. mirror. This increases the absorption by several orders of magnitude relative to that of intrinsic GaAs. Absorption losses of 1-5 dB have been reported in the case of GaAs-based MOEMS filters [57, 56]. Absorption losses are included in the power transmission such that in order to rewrite Eq. 2.14 in terms of the reflectance it is used that now

Aλ 1 = T e− + R where Aλ is the spectral absorbance. Hence Eq. 2.14 becomes

2 2Aλ (1 R) T = e− − (2.19) FP (1 R)2 + 4R sin2(δ/2) − The Lambert-Beer absorbance of a material with absorption coeﬃcient α is

Aλ = αx (2.20) where x is the distance into which the wave has propagated. For a 350 µm 18 3 slab of highly doped n-GaAs (5 10 cm− ) with an absorption coeﬃcient of 1 × 40cm− the fraction of light transmitted will be 25% corresponding to 6 dB loss. 18 3 Decreasing the doping of n-GaAs (10 cm− ) with an absorption coeﬃcient of 1 5cm− the fraction of light transmitted would be 84% or a 0.8 dB loss.

Example In Fig. 2.10 the resonance wavelength, transmission and linewidth are shown calculated for an example Micro-Opto-Electro-Mechanical Systems (MOEMS)

28 CHAPTER 2. THEORY AND DESIGN

1100

0,6

1090

0,5

1080 Transmission [dB] Transmission Linewidth [nm] Linewidth

1070

0,4

-2

1060

0,3

1050

-4

0,2

1040 Resonancewavelength [nm]

1030

0,1

1020 -6

400 450 500 550 600 650

Air gap [nm]

Figure 2.10: Plot of the ﬁlter resonance wavelength (solid black), transmission (dash blue) and linewidth (dot red) as a function of the Fabry-Pérot cavity gap.

filter based on Eqs. (2.12), (2.16) and (2.18). The MOEMS filter is a λ/2- cavity filter with a top HCG and bottom 30 pair Al0.9Ga0.1As/GaAs DBR. The reflectance and phase for the HCG and DBR have been calculated using the Rigorously Coupled Wave Analysis (RCWA) and Transmission Matrix Method (TMM) method, respectively (see Sec. 2.2.1). The filter resonance wavelength is linear with the air-cavity gap length, g, as expected from Eq. (2.12), while the transmission and filter linewidth are dominated by the variation in reflectance (mainly the HCG).

2.4 HCG-VCSEL

In the preceeding section the Fabry-Pérot filter was presented. The VCSEL consists of a vertical Fabry-Pérot cavity (of length d) made up of two mirrors between which an optical gain medium is situated. Here InGaAs QWs are used as the gain medium. Figure 2.11 shows a schematic drawing of a VCSEL with bottom DBR mirror and top DBR (left) and HCG (right) mirror. The mirrors of the Fabry-Pérot cavity provide feedback for the photon multiplication and lasing occurs as the photon absorption αi and mirror loss αm are balanced by the photon generation or modal gainh gi . Photon generation is achieved through population inversion of the gain medium,h i such that electron-hole pair recombination dominates over photon absorption. The cavity length of a VCSEL is very short which provides large spacing between longitudinal modes, but this also requires high reflectivity mirrors to compensate the short gain region. DBRs and HCGs both provides this very high reflectivity, on the order of 99.5% [24, 38, 47, 58].

29 CHAPTER 2. THEORY AND DESIGN

AlGaAs, nL GaAs, nH Oxide/Air MQW

Etop Etop DBRmirror HCGmirror

r1 r1

QuantumWell d QuantumWell r2 DBRmirror r2 DBRmirror z Ebottom Ebottom (a) (b)

Figure 2.11: Schematic drawing of (left) a DBR VCSEL and (right) a HCG VCSEL. The VCSEL consist of a bottom DBR, a quantum well active region and a top mirror, being either a DBR or HCG.

The DBR VCSEL seen in Fig. 2.11 (a) is the standard VCSEL structure. The DBR reflectance is simply controlled by the number of pairs and the Bragg wavelength λB is controlled through the stringent thickness control enabled by Metal-Organic Vapour Phase Epitaxy (MOVPE). The first demonstration of a tunable VCSEL was made by patterning the top DBR mirror into a cantilever [25]. In this way a relative tuning range of 1.6% was achieved. In the following decade VCSEL with top movable DBRs has been presented with 6.5 % and 8.5% relative tuning range for a 1550 and 1300 nm center wavelength, respectively [20, 28]. With the DBR design a wavelength tuning rate of up to 500 kHz has been experimentally demonstrated [20]. In order to increase the tuning rate further the use of a HCG reflector was proposed by Huang et al. [19]. Fig. 2.11 (b) show the HCG VCSEL where the high-index contrast is achieved by spacing the subwavelength grating from the semiconductor cavity by air or a low-refractive index medium such as an oxide. The HCG achieves the same high reflectance as the DBR, with much wider wavelength bandwidth, by the meticulous lithographic control of a subwavelength period grating [38, 59]. The HCG enables a significant thickness reduction compared to the DBR which is typically 3-5 µm thick. This both relaxes constraints on epitaxial growth, enables aperture definition through ion implantation and reduces the mechanical mass for MEMS applications [60]. The reduction of the mirror mass goes into the mechanical resonance frequency as the square root of the reciprocal thickness. Replacing the DBR by a HCG mirror the thickness is reduced by a factor of 10 and thus increase the resonance frequency by a factor of 3. HCG VCSEL tuning rates of 3 MHz has been demonstrated at 0.4% relative tuning range [19]. In this section the theory and design of the HCG-VCSEL will be presented. The reader is referred to Chap. 3 for details on the device fabrication and epitaxial structure. The major difference between the Fabry-Pérot filter and the VCSEL is the inclusion of a semiconductor gain medium. This introduces an undesired reflection at the abrupt change in refractive index between the semiconductor and air region. Hence the VCSEL must be treated as a three-

30 CHAPTER 2. THEORY AND DESIGN mirror cavity as opposed to the simpler two-mirror cavity [61]. The effects of the parasitic reflection can be circumvented by applying an anti-reflective coating - in which case the two-mirror cavity model suffice. Here we start out by presenting the well-known lasing condition of a standard VCSEL and continue to treat the HCG VCSEL in the two-mirror cavity picture as well as the three-mirror cavity picture.

2.4.1 Lasing condition The most important aspect of the laser is the light amplification by stimulated emission of radiation. From the steady state requirement that the electrical field repeats itself upon a round-trip propagation the following condition can be derived [37, 54] (Γg αi )d i(2βd θ1 θ2) 1 = r r e −h i e− − − . (2.21) | 1|| 2| where and r and θ are the reflection coefficient and reflection phase with indices refering to the top (1) and bottom mirror (2) as defined in Fig. 2.11. The phase 2πn change during a round-trip is the product of the propagation constant β = λ and the cavity length d plus the mirror reflection phases θ1,2. The product of the material gain, g, and the confinement factor Γ makes up the modal gain g [54]. The first exponential in the lasing condition, Eq. (2.21), gives the gahini requirements while the second gives the phase requirement.

Gain requirement In order for lasing to occur the following equality must hold

(Γg αi )d 1 = r r e −h i . (2.22) | 1|| 2| The mirror reflection coefficients are always less than 1 and thus the term of the exponential must be positive. The gain material is InGaAs QWs which provide both electron-hole confinement and an energy level difference engineered to the desired center wavelength λ0. The dominant optical loss is that of the highly doped regions providing low-resistance current transport as well as the scattering loss of the oxide aperture. Eq. (2.22) can be re-written as

Γg = α + α , (2.23) th m h ii where gth is referred to as the threshold material gain required for lasing. In Eq. (2.23) the mirror loss was deﬁned as

1 1 α = ln (2.24) m d r r | 1|| 2| Eq. (2.23) shows that the threshold material gain must balance the mirror and material loss, where the latter can be taken to be constant. The mirror loss on the other hand depends on the mirror reflection coefficient which is strongly wavelength dependent away from the Bragg wavelength. The modal gain g is mainly affected by the position of the QWs in the vertical direction and the modeh i confinement by the oxide aperture. The oxide aperture provides confinement of both electrons and photons. The electron confinement reduces current leakage and ensures that the gain material is under population inversion in the same

31 CHAPTER 2. THEORY AND DESIGN region as is occupied by the optical mode [62, 63]. The oxide aperture further introduces scattering for higher order modes which can be used to ensure single- mode operation.

Phase requirement From the second exponential in Eq. (2.21) follows the requirement that the round-trip electric-ﬁeld must be in-phase fulﬁlling

2πm = 2βd θ θ (2.25) − 1 − 2 where 2πn β = . (2.26) λ

For a VCSEL with DBR mirrors both mirror reﬂection phases θ1,2 are zero at the Bragg wavelength and the cavity resonance wavelength is given by Eq. 2.1.

2.4.2 Method To design the VCSEL we must have a method to calculate the mirror reflectance (covered in Sec. 2.2) and a method to calculate the modal gain, Γg. As stated by Eq. (2.23), these two quantities together with the optical loss αi determine whether lasing can be achieved or not. The CAvity Modelling FRameworkh i (CAMFR) has been used to solve for the resonance wavelength and threshold material gain [64, 65, 66]. The CAMFR package relies on the eigenmode expansion method. The refractive index and possible index variation is defined for each layer in the structure. In the eigenmode method the forward propagating electric field in each layer is a periodic function that can be written

E(x,y) = E (x,y) exp jβz (2.27) i {− } which satisfy Maxwells equation in the form of an eigenvalue problem. Equation (2.27) is the eigenmode of this eigenvalue problem and using Fourier expansion any field profile can be represented. This works well for the 1D simulations where a computationally efficient number of modes (N > 30) is needed for convergence of the single-period HCG reflectivity. For simulation of the full structure, with multiple periods of the HCG, the number of modes required for convergence makes the computation time prohibitive to the design process. For a 20 period HCG, needed to span the oxide aperture, the number of modes needed is 600. In order to keep computation time reasonable the oxide aperture is excluded from the model and thus the optical scattering losses induced by the oxide aperture are not included in the results. In order to calculate the threshold material gain of the design 2D Finite-Difference Time-Domain (FDTD) calculations have been done to include the effects of the oxide aperture [36]. For the simulation of the full structure with a DBR top mirror the calculation of the gain for a solid cavity VCSELs using CAMFR has been shown to compare to other models [65].

2.4.3 Two mirror Fabry-Pérot cavity The two-mirror cavity is conceptually the simplest. For the treatment to be valid we imagine that the internal air-semiconductor interface is coated with

32 CHAPTER 2. THEORY AND DESIGN

AlGaAs, nL GaAs, nH ARC MQW

Etop effectivereflectionplane

i(2βL1+ϕ) r1 = r1 e− HCGmirror | | L1

r1 Fabry-Perotcavity g AR-coating r3 QuantumWell d r2 DBRmirror L2

z Ebottom

Figure 2.12: Tunable VCSEL schematic (left) and model (right). The VCSEL consist of a bottom DBR, a quantum well active region, anti-reflective coating, an air-gap and a top HCG. In the model the mirrors are represented by hard mirrors with a reflectance |r|2 at a distance L and phase-shift ϕ from the physical reflection plane (see Eq. 2.11). an ideal anti-reflective coating. Figure 2.12 shows the HCG VCSEL with anti- reflective coating at the internal air-semiconductor interface. The reflection, r3, at the air-semiconductor interface is taken to be negligible.

Lasing condition

With the introduction of a passive region into the cavity the lasing condition Eq. (2.21) changes accordingly to

(Γg αa )da αp dp i(2βd θ1 θ2) 1 = r r e −h i −h i e− − − (2.28) | 1|| 2| Given that the absorption of the air region is zero and by neglecting the loss in the mirrors, the gain condition simplifies to that of Eq. (2.22). The phase condition becomes 2πn 2πm = 2 i d θ θ , (2.29) λ i − 1 − 2 i m X where the summation is over the optical length of all the layers making up the cavity. At the Bragg wavelength the DBR reflection phase θDBR = 0, while the HCG reflection phase θHCG can be taken as a correction to the air-gap given by λm θ . Eq. (2.29) can be used in the design of the HCG-VCSEL epi- − 4πn HCG structure to be resonant at the wavelength λ0. From the phase condition Eq. (2.29) the cavity resonance wavelength becomes

4π λm = Deﬀ . (2.30) 2πm + ϕ1 + ϕ2

Here Deﬀ has been deﬁned as the total optical length of the cavity. The shift in wavelength with a change in the air-gap length, also referred to as the tuning

33 CHAPTER 2. THEORY AND DESIGN

Section τ ngL ϕ HCG 3.9 fs 0.55λ0 2.04π Air-gap 0.46λ0 0 AR-coating 0.25λ0 0 Semiconductor 1.78λ0 0 30-pair DBR 11.8 fs 1.67λ0 6.69π

Total, Deﬀ 4.71λ0 8.7π

Table 2.1: Reflection delay τ, penetration depth L and constant reflection phase ϕ for the two types of mirrors. The DBR is a 30-pair Al0.9GaAs/GaAs stack designed for λ0 = 1060 nm. The HCG is a 280 nm thick GaAs slab with a grating period of 460 nm and duty cycle of 72%. efficiency, can then be written as ∂λ 4π λ m = = m (2.31) ∂g 2πm + ϕ1 + ϕ2 Deff Eq. (2.31) shows that the tuning efficiency is inversely proportional to the effective cavity length Deff , which provides the guideline that the cavity length must be minimized [28]. The full spectral range

2 λm FSR = λm λm+1 = (2.32) − 2Deff is inversely proportional to the effective cavity length. The FSR sets the upper limit on the continous wavelength tuning range. For the HCG-VCSEL design ∂λm seen in Tab. 2.1 the tuning efficiency is ∂dair = 0.212 and the FSR is 113 nm. In the case that electro-static actuation is used in changing the air-gap, the 1 absolute change is limited to 3 of the initial air gap thickness due to the pull-in instability. Then the maximum tuning range becomes ∂λ 0.46λ ∆λ = m ∆g = 0.212 0 = 0.033λ = 35nm (2.33) ∂g · 3 0 which is well within the FSR. Hence for electro-static actuation the FSR will not be the limiting factor for a fundamental-cavity design. The tuning range can be extended by increasing the initial air-gap distance, which will slightly decrease the tuning efficiency. Since pull-in limits the tuning range it can be nearly doubled by increasing the air-gap thickness to the next integer mode, as the tuning efficiency and FSR only decrease by 10% in the given example (referring to Tab. 2.1 the total cavity length Deff only increase by 10%). Recalling that the 99.5% bandwidth of the Al0.9GaAs/GaAs DBR was 80 nm, pull-in is expected to set the upper limit on the tuning range.

Mode confinement The field distribution throughout the device structure or the standing wave pattern at lasing was calculated using CAMFR. Fig. 2.13 shows an example of a standing wave pattern of a HCG-VCSEL with a λ0/2 air-gap, an ideal anti- reflection coating, an oxide aperture and 3 QWs where the cavity thickness, d, has been chosen such that phase condition, Eq. (2.21), is fullfilled at 1060 nm.

34 CHAPTER 2. THEORY AND DESIGN

CavityMode λ =1060nmGaing =147cm-1 1 0 th 5

0.8 oxide 4 HCG aperture DBR

QW 0.6 AR 3

0.4 2

RefractiveIndex Air-gap 0.2 1

Electric FieldMagnitude(au.)

0 0 0 0.5 1 1.5 2 z-axis [mm]

Figure 2.13: Plot of the standing wave electric field in a HCG-VCSEL with 30-pair Al0.9GaAs/GaAs DBR with λB = 1060 nm and HCG with 280 nm thickness, 460 λ0 nm period and 72% duty cycle. The HCG-VCSEL has a 530 nm air-gap and 4n ideal single-layer anti-reflection coating. The oxide current aperture and 3 QWs both aligned to the electric field anti-node.

Fig. 2.13 shows how the field anti-node is aligned to the QW such that the material threshold gain is minimum. In this example the oxide aperture is also placed at the field anti-node in order to maximize optical confinement. The oxide position is a trade-off between optical scattering loss from the thin oxide aperture and optical confinement [67]. Strong optical confinement results from placing the oxide aperture at the field anti-node at the expense of higher optical scattering loss. Placing the oxide aperture at the field node the optical scattering loss is smaller, but this also results in poor optical confinement why the mode will spread over a larger mode volume. This will decrease the overlap of the optical mode with the region of population inversion and increase optical loss through absorption. The 1D simulation shows a 15% reduction in the threshold material gain with the oxide aperture placed at the field node. In order to optimize the position of the oxide aperture in terms of lateral confinement 2D simulations has been done.

Output power The laser output power above threshold is given by

hν P = η (I I ) (2.34) q − th where η is the diﬀerential quantum eﬃciency. This is the total power output, but normally it is the power output of either the top or bottom mirror that is of interest. The light escaping the cavity through the mirrors is determined by the mirror transmittivities and if they are not equal the power output out of the two mirrors will not be either. The fractional power output of mirror 1 is

35 CHAPTER 2. THEORY AND DESIGN

100

99.9

99.8

99.7 Reflectance [%]

99.6 HCG DBR 99.5 1020 1030 1040 1050 1060 1070 1080 1090 1100 Wavelength [nm]

Figure 2.14: The reflectance for a 30-pair Al0.9GaAs/GaAs DBR with λB = 1060 nm and HCG with 280 nm thickness, 460 nm period and 72% duty cycle. determined by t2 F = 1 (2.35) 1 (1 r2) + r1 (1 r2) − 1 r2 − 2 where the indices refers to the top (1) and bottom (2) mirror. Fig. 2.14 shows the reflectance of a 30-pair Al0.9GaAs/GaAs DBR with λB = 1060 nm and HCG with 280 nm thickness, 460 nm period and 72% duty cycle. The reflectance of the HCG has a high bandwidth characterized by two resonances. As seen from Fig. 2.14 the HCG reflectance is higher than the bottom DBR outside a 40 nm bandwidth. This would result in a roll-off in the power output through the top mirror, but it remains to be experimentally demonstrated what the upper limit is to the HCG reflectance. Hence this roll-off may not be observed in experiments. The high HCG reflectance could be used to an advantage in bottom emitting devices. This is viable for VCSEL beyond 980 nm, but at lower wavelength optical absorption in the GaAs substrate will limit the power output. Another solution would be to use Al2O3/GaAs bottom mirrors, that have a much broader bandwidth, to ensure top emission.

2.4.4 Three mirror Fabry-Pérot cavity The refractive index continuity between the active and passive part of the laser cavity, seen in Fig. 2.12, must be included to properly model the cavity resonance. The large index contrast between the gain region and the air region, 2 with no anti-reflective coating present, will cause a reflection of r3 = 30%. In the preceeding section Sec. 2.4.3 a two mirror Fabry-Pérot laser| cavity| was treated, by neglecting the reflection at the semiconductor-air interface. This will be shown to be a valid assumption in the case of an anti-reflective coated interface. Removing the anti-reflective coating, two different cases arise where either the field magnitude is largest in the air-gap or in the semiconductor [68].

36 CHAPTER 2. THEORY AND DESIGN

1 4

3/4λ 0.9995 0 2

0.999 0 [] [radians] eff eff θ 0.9985 −2 Reflection, R 0.998 −4 Reflection phase,

0.9975 1/2λ −6 0

0.997 −8 200 300 400 500 600 700 800 900 1000 1100 Air−gap, d [nm] air

Figure 2.15: Plot of the effective reflectance, Reff and the reflection phase, θeff , for the semiconductor-air-HCG effective mirror.

The two situations are referred to as the air-coupled and the semiconductor- coupled cavity, respectively. For the total round-trip phase to add up we still adhere to the requirement of Eq. (2.29), namely that the total cavity optical length is a integer multiple of λ0/2. Following the treatment in [54] the three-mirror cavity can be treated in the same way as the two-mirror cavity, where the air-HCG section is replaced by an effective reflectance, reff , that includes the semiconductor-air interface t2r e j(2βg θ1) r = r + 3 1 − − . (2.36) eff 3 j(θ1 2βg) 1 + r3r1e − where nGaAs 1 2 r3 = − and t3 = 1 r3. (2.37) nGaAs + 1 − q Figure 2.15 shows Eq. (2.36) plotted versus the air-gap length βg. In Fig. λ 2.15 there are two distinct regions. For 2 m there is an minimum in reflectance and the slope of the reflection phase is highest. This corresponds to the air- λ coupled case. For 4 (2m + 1) there is a maximum in reflectance and the slope of the reflection phase is smallest. This corresponds to the semiconductor-coupled case. The phase condition for the coupled cavity is 4π 2πm + ϕ = (nd + nL ) θ (g) (2.38) DBR λ DBR − eff Deff from which the tuning efficiency follows| as {z } ∂λ λ2 ∂θ m = m eff . (2.39) ∂g −4πDeff ∂g

37 CHAPTER 2. THEORY AND DESIGN

Refractiveindex Electricfield

TopHCG TopHCG TopHCG

0.4

0.8

-xs[m] Z-axis[

1.2

1.6

BottomDBR BottomDBR

2 BottomDBR (a) (b) (c)

Figure 2.16: Plot of the refractive index (solid) and electric ﬁeld (dashed) from the top HCG to the bottom DBR for an (a) extended cavity (b) air-coupled cavity (c) semiconductor-coupled cavity.

From Eq. 2.39 it can be concluded that the wavelength change is proportional to the eﬀective mirror reﬂection phase change.

Air-coupled cavity For the air-coupled cavity the optical thickness of the air-region must be ng = λ 2 m. The air-coupled cavity has the advantage of a high tuning efficiency, while the drawback is that the optical field is highest in the air-region where the ∂θeff optical gain is zero. The derivative of the reflection phase is found to be ∂g = 0.0406/nm and inserting in Eq. (2.39) the tuning efficiency is calculated to be −0.927 using the values in Tab. 2.2.

Semiconductor-coupled cavity

λ For the semiconductor-coupled cavity the optical thickness must be ng = 4 (2m+ 1). The semiconductor-coupled cavity has the advantage of a low threshold material gain, while the drawback is that the tuning efficiency is low. The derivative ∂θeff of the reflection phase is found to be ∂g = 0.0035/nm from which the tuning efficiency results as 0.086. −

2.4.5 Summary In sections 2.4.3 and 2.4.4 three possible cavity design has been discussed, namely the (a) extended cavity, (b) the air-coupled cavity and (c) the semiconductor coupled cavity. In order to tune the physical length of the cavity, part of it must be air and this results in an unwanted reﬂectance between the air and semiconductor region. This situation can be analyzed as a three-mirror

38 CHAPTER 2. THEORY AND DESIGN

Structure Air Cavity Dtot Eﬃciency Range gmin 1 λ0 λ0 λ0 [nm/nm] [nm] [cm− ] Ideal ARC 0.707 1.779 4.75 0.212 (0.213) 34 (37) 140 AlOx ARC 0.707 1.779 4.75 0.212 (0.162) 26 (29) 120 Air-coupled 0.457 2.025 4.70 0.927 (0.474) 77 (42) 327 Semiconductor-coupled 0.707 1.775 4.74 0.086 (0.069) 17 (18) 98

Table 2.2: shows the tuning efficiency and range for different HCG-VCSEL cavity design together with the minimum gain (at λ0 = 1060 nm). The range is limited by electro-static pull-in to 1/3 of the initial gap spacing. The tuning range value in paren- thesis is the numerical value from CAMFR. The HCG initial phase is θHCG = −0.535 and the effective length LHCG = 0.55λ0 and the bottom DBR 30 pair GaAs/Al0.9GaAs has an effective length of LDBR = 1.67λ0. cavity. Table 2.2 compares the tuning efficiency, range and minimum threshold material gain for an extended cavity with ideal anti-reflective coating, extended cavity with Al2O3 anti-reflective coating, air-coupled cavity and semiconductor- coupled cavity. The standing wave pattern can be seen in Fig. 2.16, which shows how the electric field is more strongly confined in the air region for the air-coupled cavity. From Tab. 2.2 it is seen that the tuning efficiency of the extended cavity is twice that of the semiconductor-coupled cavity, while the minimum threshold material gain is only 20% larger. The tuning efficiency of the air-coupled cavity is several times higher than the semiconductor-coupled cavity, but in practise it is limited by high threshold material gain. Tab. 2.2 shows the tuning efficiency for different design computed from the analytical expression in Eq. (2.31) compared to the result computed by CAMFR (in parentheses). For a VCSEL structure with a perfect anti-reflective coating, the analytical result of Sec. 2.4.3 matches the numerical result. From the analytical and numerical modelling it is found that there is a trade-off between low threshold material gain and high tuning efficiency for the three-mirror cavity. In order to overcome this limitation the internal semiconductor-air interface can be coated with an anti-reflective coating. The refractive index of the anti-reflection coating should preferably be as close to √ncav = √3.5 = 1.87 as possible. For a fully epitaxial solution the oxide of AlAs can be used which has a refractive index close to 1.6. From Tab. 2.2 this is seen to result in a decrease of the tuning efficiency by 24%. Nevertheless the tuning efficiency is still 60% larger than the semiconductor coupled cavity, while the threshold material gain is only 22% larger. Fig. 2.17 shows a plot of the threshold material gain as function of the wavelength detuning, λ λ0, for the Al2O3 coated extended cavity, air-coupled cavity and semiconductor-coupled− cavity. Again the threshold material gain is seen to be lowest for the semiconductor-coupled cavity, but the extended cavity shows are more flat curve.

39 CHAPTER 2. THEORY AND DESIGN

600 Semiconductor coupled Air coupled Extended cavity 500 ] −1 [cm

0 400

300

200 Threshold material gain, g 100

0 −30 −20 −10 0 10 20 30 Wavelength detuning, λ−λ [nm] 0

Figure 2.17: Plot of the threshold material gain as function of the wavelength detuning, λ − λ0, from the intial wavelength λ0 for the three possible cavity conﬁgurations: semiconductor coupled (solid), air coupled (dashed) and extended cavity (dotted)

2.5 Electro-static actuation

The most straight-forward way to implement tuning of the air-gap distance is through electro-static actuation. This only requires electrical contacts to the top and bottom mirrors, both of which should be conductive, and a mechanical suspension of the top mirror. Fig. 2.18 shows a schematic drawing of how this could be implemented. The mechanical suspension (spring) counters the electrostatic forces and the gap distance can then be controlled through what is an electrostatic actuator. Piezo-electric actuation was also considered at the outset of the project. This would enable larger tuning range, but also require more elaborate process development and it is not yet clear whether meaningfull actuation ranges can be achieved [33].

2.5.1 Static operation

The electro-static tuning of the MEMS VCSEL can be described through the electro-static force on the parallel-plate capacitance between the HCG and the substrate. In the derivation of the electric force the fringing field is assumed negligible. In Fig. 2.18 the grating structure of the HCG mirror is shown. The grating consists of bars and air spacing and because the mirror is not solid fringing fields will exist between the bars. Due to the symmetry the electric field profile in the air-gap will be very similar to that of a solid mirror and only perimeter will contribute to the fringing field. The displacement of the HCG

40 CHAPTER 2. THEORY AND DESIGN

Support

Spring HCGmirror Spring t + HCG Fabry-Perotcavity g V HCGmirror L DBRmirror W -

Figure 2.18: Schematic of the electro-mechanical design of the ﬁlter. mirror can be controlled by electrostatic actuation using a voltage source. The force acting on a capacitive element of area A is [69]

ǫAV 2 F = DC (2.40) el 2g2 where the gap distance g = g w (2.41) 0 − can be written in terms of the initial gap distance g0 and the mirror displacement w. The mechanical force, Fmech = kw and the electrical force Fel balance each other at a gap distance of ǫAV 2 g = g DC . (2.42) 0 − 2kg2 Eqs. (2.40) and (2.42) shows the non-linear behaviour of the voltage-controlled electro-static actuator. Eq. (2.42) has two equilibrium gap distances g until it reaches the pull-in instability at gPI above which the electrostatic force is larger than the mechanical restoration force for all g. From the requirement that the 2 tangential of the two forces are equal this found to occur for gPI = 3 g0 at a voltage of 3 8kg0 VPI = . (2.43) r27ǫA The above analysis readily applies to the case of the HCG VCSEL which has the same electro-mechanical structure. In the case of the HCG VCSEL with anti-reflective coating (ARC) the capacitance changes due to the presence of an isolating oxide. This can be accound for in substituting g = g′ t in the above − ox equations, where g′ is the physical air gap distance and tox the coating of the oxide. The function of the mechanical suspension is to allow the mirror to move in the vertical direction, while maintaining its flatness. Hence it is mainly the mechanical suspension, the spring, that is deforming under the applied electro- static load. The mirror is taken to be a rigid plate, which is connected to a solid support by four fixed-guided beams. Simply due to the larger size of the mirror it will have a higher stiffness. The stiffness of a fixed-guide beam is found

41 CHAPTER 2. THEORY AND DESIGN solving the Euler equation [69]

EW H3 K = (2.44) (χL)3 where E is the Youngs modulus (EGaAs = 85.9 GPa), W is the width, H the thickness and χL the length of the spring. In the mechanical design of Fig. 2.18 the HCG is attached to 4 springs why the total spring constant, k is four times that given by Eq. (2.44).

Electrostatic spring softening The spring suspension will also experience a distributed electro-static force

∂4w(x) ǫ(χL)V 2 EI = q(x) = (2.45) ∂x4 2(g w(x))2 0 − where w(x) is the displacement, g0 the gap distance at zero voltage V = 0. Through a Taylor expansion of the right-hand side of Eq. (2.45) around w(x) = 0 the differential equation is linearized, resulting in an electrostatic spring constant 2 ǫaVDC Kelec = 3 (2.46) − g0 The sign in Eq. (2.46) shows that increasing the electro-static force, as given by Eq. (2.40), results in a decrease of the beam stiffness. This results in a decrease of the resonance frequency at large-signal modulation and the electro-static spring softening must be taken into account when estimating the displacement versus voltage characteristic of the MEMS. Fig. 2.19 shows a plot of the gap 1 distance versus voltage for a 2 λ0-cavity. The displacement has been computed from the analytical expression Eqs. (2.44) and (2.46) and by using a finite- element model (FEM) implemented in COMSOL. The FEM is implemented using a moving mesh to account for the change in gap distance when computing the electro-static force from which the mechanical deformation is computed. The relative error of the displacement is reduced by half using the first order estimate of the electro-static spring softening.

2.5.2 Dynamic operation The dynamics of the mirror is determined by Newton’s second law which cou- ples the mirror mass acceleration to the spring constant. Due to squeeze ﬁlm damping, the dynamic response for the actuator will be damped in operation at atmospheric pressure, while in vacuum the actuator will behave as a simple oscillator due to the abscene of a frictional force [70]. The mirror can be analyzed in terms of the classical harmonic oscillator with damping. The equation of motion of the mirror may in dimension-less form, be expressed as [69, 71, 72]

ω 4 V 2 ω2 u¨ + 0 u˙ + ω2u = 0 (2.47) Q 0 27 V (1 u)2 PI − where u = z/g0 is the normalized deﬂection, Q is the quality factor, ω0 is the angular resonance frequency, V the bias voltage and VPI the pull-in voltage.

42 CHAPTER 2. THEORY AND DESIGN

0.7 Analytical FEM 0.65

0.6

0.55

0.5 Gap distance [nm] 0.45

0.4

0.35 0 5 10 15 20 Voltage [V]

Figure 2.19: Plot of the electro-mechanical deﬂection versus the capacitor voltage. The beam thickness is 0.28 µm, the width 1.5µm and the HCG mirror has a sidelength of 12µm.

The driving force of the harmonic oscillator is the electro-static non-linear term at the right of Eq. (2.47). Doing a series expansion of the right-hand side of Eq. (2.47) in terms of the normalized deﬂection u the electro-static driving force per unit mass, Fel′ writes as

2 2 4ω0 V 2 3 4 F ′ = 1 + 2u + 3u + 4u + (u ) . (2.48) el 27 V O PI For the linear harmonic oscillator a forced oscillation will result in a time- dependent deﬂection of

4 V 2 ω2 u(t) = 0 cos(ωt φ) (2.49) 27 V 2 2 − P I (ω2 ω2) + (ω2/Q) 0 − 0 q which has a peak at ω = ω0, its magnitude proportional to the quality factor Q. The phase lag of the deﬂection amplitude to the driving force is given by

1 ω/ω tan φ = 0 (2.50) Q ω2 ω2 0 − The first higher order term (2u) of Eq. (2.48) results in a reduction of the spring constant (see Eq. (2.46)), why it is commonly referred to as the electro- static spring softening. The second (3u2) and third (4u3) higher order terms are additional corrections to the spring constant. The correction term to the third order is often referred to as the Duffing constant as it appears in the Duffing

43 CHAPTER 2. THEORY AND DESIGN equation. The higher order terms mainly aﬀect the behavior near resonance shifting, which is seen as hysteresis in the amplitude frequency response [70]. Hence we note that the non-linear terms turns up as a correction to ω in Eq. (2.49). Generally downwards tuning (blue-shifting) from the initial emission wavelength is considered applicable to MEMS VCSEL when static operation is considered. Here we show that by considering dynamic operation upwards wavelength tuning (red-shifting) can be achieved.

Resonance frequency The resonance frequency of the mirror can be estimated as

4K ω = (2.51) r m where m is the mass m = ρL2H (2.52) and K is the total spring force. Fig. 2.20 shows the resonance frequency versus the mirror sidelength for a beam length fixed to the mirror sidelength. The mechanical resonance frequency increases into the 100 kHz range below a mirror sidelength of 40 µm. The inset in Fig. 2.20 shows the COMSOL model of the mirror with a color-graded vertical deformation (red = largest deformation, blue = no deformation). This shows how the mirror stay planar to a large extent, while it is the beams that carry the deformation. The design in Fig. 2.20 is for the Fabry-Pérot filter, while similar results apply to the HCG-VCSEL. The HCG-VCSEL is not as the Fabry-Pérot filter limited by the focusing and coupling of the filtered light beam and smaller mirrors can be used. This increases the obtainable mechanical resonance frequency towards the MHz regime.

44 CHAPTER 2. THEORY AND DESIGN

4 10

[kHz] 3 10

2 10

Resonancefrequency,f

1 10 1 2 10 10 Mirrorsidelength,L [m m]

Figure 2.20: Plot of the resonance frequency for a HCG Fabry-Pérot cavity as function of the mirror sidelength L calculated using COMSOL. The beam width is ﬁxed at W = L/10.

45 Chapter 3

Device fabrication

In this chapter the device fabrication is presented together with the measurements done in order to qualify the process. The major part of the thesis work has been put into process development. A process for the fabrication of monolithic MOEMS has been developed based on an AlInP sacrificial process. Fur- thermore, growth of an In0.3Ga0.7As Multiple Quantum Well (MQW) has been developed in order to fabricate a tunable VCSEL at 1060 nm. The epitaxial growth is covered in Sec. 3.1 where an accounts is given for both the development of strained InGaAs MQWs and lattice-matched InAlP together with considerations on growing the full epitaxial structure for the VCSELs. InAlP is used as a sacrificial layer to define the tunable air-gap and since the anisotropic wet etching of InAlP is not covered in literature, a detailed account is given in Sec. 3.2. This is followed by another part of the process development work which has been the patterning of subwavelength gratings. The different masking and patterning techniques that have been investigated are described in Sec. 3.3. The chapter ends with a description of the process flow for making the Fabry- Pérot filters, VCSELs and HCG VCSELs that are part of this thesis. This is covered in Secs. 3.4-3.6. The process flow for the DBR VCSEL was developed prior to this work.

3.1 Epitaxial growth

The goal of this project has been to realize a tunable VCSEL with a center wavelength at 1060 nm. Within telecommunication emphasis has been put on 850, 980, 1310 and 1550 nm, while 1060 nm has mainly found its use as seed laser diode in second harmonic generation of green light and supercontinuum generation in optical ﬁbers. For VCSELs in this wavelength, InGaAs grown on GaAs is favoured due to the high index contrast of AlGaAs/GaAs DBRs. The disadvantage is that InGaAs is not lattice-matched to GaAs and the strain give rise to growth instabilities. InGaAs Quantum Well (QW) gain material is used for 980 nm VCSELs where the strain increases the diﬀerential gain which in return allows for higher modulation frequencies to be reached. The commercial use of 1310 nm VCSELs has made several research groups interested in pushing the boundary for growth of InGaAs QWs [73, 74, 75, 76]. The two main approaches in growing long-wavelength InGaAs QWs has been to either

46 CHAPTER 3. DEVICE FABRICATION suppress growth defects by lowering the growth temperature or to use strain- balancing barriers. In this work we established the growth parameters at DTU for growing 1060 nm In0.28Ga0.72As MQW as presented by Hou et. al. using GaAsP barriers for strain-balancing [77]. The growth was done using an Emcore D-125 Turbodisc R equipped MOVPE rotating disk reactor. The growth pressure was fixed at 80 Torr. Epi-ready 50 mm (100) GaAs wafers with the major flat cut along 01¯1¯ were used for all growths. The MOVPE was equipped with hydrogen (H ) as carrier gas. For 2 the group III the precursors trimethylgalium (TMGa), trimethylindium (TMIn), trimethylaluminum (TMAl) were used and for the group V arsine (AsH3), phosphine (PH3) and tributhylphosphine (TBP). The n-dopant was disilane (Si2H6) and the p-dopant carbon tetrabromide (CBr4). The epitaxial growth for all devices was done on polished n-doped GaAs grown by the vertical gradient freeze method. As has been noted in the literature the substrate quality is key in order to obtain good epitaxial wafers [74]. The same recipe on different substrates would yield completely different growth results both in term of composition and growth instabilities. We have painstakingly found the same result.1 Epitaxial growth is done in the mass transport limited regime with a high partial pressure of the group V constituents. This has the consequence that the growth rate is limited by the diffusion of group III constituents to the V-rich GaAs surface. The solid composition, xs, of ternary materials AxB1 xC with a single group V element is controlled through the vapor phase composition− [A] xv = [A]+[B] . Controlling the flow rate of the group III pre-cursors, at complete pyrolysis efficiency, give direct control of the vapor phase composition. The complete decomposition of TMIn and TMGa happens at low temperatures of 350◦C and 475◦C, respectively [78]. The low temperature needed to decompose TMIn makes it possible to grow InGaAs at lower temperatures. Lowering the temperature reduces the migration length of In atoms on the surface and this is believed to suppress the transition to island growth mode. In this study we chose a growth temperature of 580◦C for the InGaAs QWs and GaAsP barriers. In order to grow the barriers at the same temperature as the QWs, to avoid long growth interrupts, TBP was used instead of PH3. Very high temperature, greater than 850◦C, is required for full PH3 pyrolysis, while a much lower temperature around 450◦C is required for TBP [78]. The incomplete pyrolysis of PH3 at low growth temperatures makes the solid composition xs highly non- linearly dependent on the vapor phase composition xv. Since pyrolysis of TBP is achieved at lower temperatures, control of the As/P ratio is more linearly dependent and higher P-concentration can more easily be achieved [78]. Al- GaAs growth was done at higher temperatures (720◦ for the DBRs) in order to suppress the presence of oxygen which would otherwise result in poor layer quality.

1Poor crystal quality GaAs leads to surface rougness, and thus lower X-Ray Diffraction (XRD) signal, while the Photoluminescence (PL) does not suffer unless the surface roughness triggers growth instabilities. A large number of wafers from the same ingot would show a high PL-signal at the edges and low in the center with a hazy surface finish. The exact same growth on a wafer from another ingot would show a specular surface finish and high average PL across the full wafer.

47 CHAPTER 3. DEVICE FABRICATION

PL 14

emissionwavelength[ Criticalthickness,hc

Thickness,h[nm]

4 0.2 0.23 0.26 0.3 Indiumcontent,x[]

Figure 3.1: Contour plot of the PL emission wavelength as a function of In-content and QW thickness. The dashed line show the critical thickness with m = 2.

3.1.1 InGaAs MQW To increase the emission wavelength from InGaAs QWs the In-content and or the QW thickness should be increased. Fig. 3.1 shows the wavelength corresponding to the conduction band electron to heavy-hole bandgap. From the Matthews- Blakeslee theory the critical thickness, hC , is given by

1 ν aGaAs √2hC hC = − ln + 1 (3.1) 1 + ν m√2π f aGaAs | | where aGaAs is the lattice constant of the GaAs substrate, ν the Poisson ratio, f the lattice mismatch and m is 1, 2 or 4 depending on whether the thin film is a single layer, embedded in the substrate or part of a multilayer structure [79, 80]. In order to arrive at Eq. (3.1) we have assumed a burgers vector of b = a0/√2, a misfit dislocation angle of α = 60◦ and slip direction λ = 0◦ relative to the 111 plane. Fig. 3.1 shows that it should be possible to increase the emission {wavelength} beyond 1060 nm with an In-content above 25%. This is close to the thickness at which the strain is accommodated by misfit dislocations. Increasing the In-content is by itself a challenge since high strain limits the incorporation of In to around 30% at 650◦ [81]. Growth to thicknesses close to the critical thickness predicted by the Matthews-Blakeslee theory have been shown possible [74]. This can be done by supressing the formation of misfit dislocations that forms the basis of the Matthews-Blakeslee theory. There are two distinct strategies undertaken in order to push the PL emission to longer wavelengths: 1) decrease misfit dislocation formation, 2) reduce the effective strain. In the first case GaAs is used as a lattice-matched barrier material, while in the second case GaAsP is used as a strain-compensating barrier material due to its opposite (tensile) biaxial strain. Common to both approaches is that in order to limit transition from 2D to 3D growth (island

48 CHAPTER 3. DEVICE FABRICATION nucleation) it is generally accepted that a low growth temperature, high growth rate and V/III ratio2 should be used in order to lower the In migration/diffusion length [76]. Lowering the migration length of In suppress the coalescense of In-rich clusters. For the first case the low growth temperature furthermore suppress the relaxation of misfit dislocations. High growth temperatures are on the other hand associated with better crystal quality. For the second case a phase separation can occur due to the presence of both InGaAs and GaAsP. The lower the temperature the larger is the miscibility gap [82]. To avoid the phase separation associated with the miscibility gap the growth should be driven far from thermodynamic equilibrium. High growth rates together with high V/III ratio can be used in order to suppress phase separation. We have succeeded in growing high-quality 5MQW active material using the Zero Net Strain (ZNS) approach where the tensile strain of the GaAsP barrier layer compensate the compressive strain of the InGaAs active layer according to ǫ d 2ǫ d = 0 (3.2) QW QW − Barrier Barrier where ǫ and d are the biaxial strain of the QW and barrier thickness, respectively. For In0.3Ga0.7As the compressive strain is ǫxxyy = 2.1% and using GaAs0.8P0.2 with a tensile strain of ǫxxyy = 0.7% the ZNS condition for dQW = 8 nm is reached with dBarrier = 23 nm. In order to achieve strain balancing the growth time for the GaAsP barriers was tuned according to the P-content fitted from the XRD measurement of InGaAs/GaAsP calibration growths. The solid composition of GaAs1 xPx is highly dependent on the vapor phase − ratio between AsH3 and PH3 for low temperatures < 650 ◦C. Since the GaAsP strain-compensating barrier layers are grown at the same temperature as the InGaAs QW (580◦); this favors TBP, which show a reduced dependence on the vapor phase composition of the group V [78]. The best results for the barrier GaAs0.8P0.2 in terms of surface quality was achieved by using TBP as precursor with the same growth rate as the QW. A screening experiment for the InGaAs QW in terms of the growth temperature together with the TMIn and AsH3 flow rates was done. From this screening experiment two trends were seen. First lowering the temperature was required to avoid In segregation in the QW which resulted in a shoulder on the long-wavelength side of the PL peak. Secondly increasing the growth rate and V/III ratio increased the PL intensity. While the positive effect of increasing the growth rate can be understood in terms of the suppression of phase separation the positive effect of the V/III ratio is not well understood. The optimum growth parameters was found to be a growth rate of 8 Å/s and a V/III ratio of 150. Increasing both the growth rate and the V/III ratio at the same time is limited by the maximum AsH3 flow rate. Lowering the growth rate would allow the V/III ratio to be increased, which has been used in InGaAs growth with GaAs barriers [74]. For GaAsP strain-compensated barriers we have found island nucleation at low growth rates of 2 Å/s. Fig. 3.2 shows the rocking curve from an XRD measurement around the Bragg angle of the GaAs substrate together with the PL intensity spectrum (inset) of a ZNS 5MQW In0.3Ga0.7As test growth. The clear superlattice fringes seen on the rocking curve is a sign of

2In this text we deﬁne the V/III ratio in terms of the molar ﬂow rates at the chamber inlet. The V/III ratio is an often used variable that albeit not saying anything of the partial pressure at the surface it the actual parameter we control.

49 CHAPTER 3. DEVICE FABRICATION

D613

100000

1 Signal [V]

10000

superlattice fringes 950 1000 1050 1100 1150

W avelength [nm ]

1000

100 Intensity [au] Intensity

InGaAs GaAsP

-6000 -4000 -2000 0 2000 4000

Relative Rocking Angle ["]

Figure 3.2: Plot of the rocking curve for a ZNS 5MQW In0.30Ga0.70As with GaAs0.83P0.17 barriers (no cladding). The InGaAs/GaAsP superlattice thickness is 31.8 nm. The inset shows the PL intensity with a peak at 1063 nm and 21.7 nm FWHM (24 meV). sharp layer transitions. The superlattice peak FWHM is 120".The period of the superlattice modulation peaks at the left side of the substrate peak corresponds to a thickness of 27.5 nm. The inset shows the room-temperature PL spectrum with at peak intensity at 1071 nm and 29 nm FWHM.

3.1.2 VCSEL

Si-doped Al0.9Ga0.1As/GaAs n-DBRs was grown as bottom mirrors. The high Al-content gives a moderate refractive index contrast, while still being low enough for the oxidation rate to be orders of magnitude lower than the oxidation layer (Al0.98G0.02aAs). The GaAs is grown at 13 Å/s and the Al0.9Ga0.1As at 9 Å/s. In order to calibrate the growth rate a 11.5 pair Al0.9Ga0.1As/GaAs DBR was grown and the reflectance spectrum fitted using the TMM. From such a growth and fit routine the growth rate can be determined to within 0.5 Å/s. The fitting routine was based on fixing the refractive index and only± varying the thickness[83]. As cladding layer GaAs was chosen since it can be grown at higher crystal quality at the low temperatures used for the MQW growth than Al0.3Ga0.7As - which on the other hand would give better carrier confinement. The MQW and cladding are un-doped in order to limit absorption losses. A 55 nm Al0.98Ga0.02As oxidation layer was placed close to the field anti-node the exact position optimized to give the lowest threshold current by balancing optical confinement and scattering losses. The thickness of the oxide aperture layer was choosen such that the oxidatin rate would not depend on deviations in

50 CHAPTER 3. DEVICE FABRICATION

Figure 3.3: Plot of the left: PL peak wavelength λ, right: FWHM for a ZNS 5MQW In0.30Ga0.70As with GaAs0.83P0.17 barriers (D613). The sample has been excited with a 532 nm CW laser and the PL measured using an InGaAs detector. the grown thickness [84]. Above the oxide aperture layer the GaAs was doped 18 3 5 10 cm− in order to allow low-resistance current spreading. The GaAs current× spreading layer was followed by the InAlP sacrificial layer and the top Si-doped GaAs HCG layer. The epitaxial structure grown is shown in the results section 5.3 Figure 3.3 shows the peak wavelength and FWHM of a ZNS 5MQW In0.30Ga0.70As test growth with GaAs0.83P0.17 barriers. The same growth parameters were used for the final HCG-VCSEL growth. The average wavelength is 1062 nm with a standard deviation of 8 nm across the wafer. The wafer surface is specular and the surface planar with a very low density of growth defects. Fig. 3.4 shows the measured and simulated XRD of the full epitaxial structure. The InGaAs/GaAsP superlattice is clearly visible and the fitted values are close to that of the test growth, see Fig. 3.2. The pendelösung fringes splitting the GaAs substrate peak originates from the AlGaAs/GaAs superlattice. The good agreement between the simulated and measured XRD with regard to the epi- design parameters shows that good layer control has been achieved. The inset in Fig. 3.4 shows the fitted values of the simulation where the thickness and composition has been fixed for all layers except GaAsP and InGaAs.

3.1.3 InAlP

In1 xAlxP was grown using PH3, TMIn and TMAl. In order to achieve lattice- − matching to the GaAs substrate the composition should be In0.48Al0.52P. The InAlP was grown at temperatures from 610 ◦C to 700 ◦C. Comparing growths at 610, 650 and 700 ◦C all had a specular surface. Hence we are able to grow InAlP with good surface morphology at low growth temperatures [85]. The growth temperature was ﬁxed to 610 ◦C to match the growth temperature of the MQW. Fig. 3.5 shows the peak separation measured from XRD on test growths of 530 nm InAlP capped with 280 nm GaAs. The right axis shows the corresponding lattice mismatch - which was calculated from the diﬀerential form of Bragg’s law

∆a = cot(θB,GaAs)∆ωGaAs InAlP (3.3) a − −

51 CHAPTER 3. DEVICE FABRICATION

Material Thickness Composition (%)

Simulation

100000

GaAs 280 --

Measured

AlGaInP 562 Al: 52.0000 & Ga: 0.000

AlGaAs 176 Al: 98.0000

GaAs 201 --

AlGaAs 98 Al: 98.0000

10000

GaAs 159 --

GaAsP 24 P: 18.3750

InGaAs 7.2 In: 27.0000

GaAs 75 --

AlGaAs 89 Al: 90.0000

1000

GaAs 350000 -- XRDIntensity

100

-6000 -4000 -2000 0 2000 4000

Relative Rock Angle (")

Figure 3.4: Plot of the XRD of the full epitaxial HCG-VCSEL structure.

where a is the substrate lattice constant, ∆a the lattice mismatch, θB,GaAs the substrate peak and ∆ωGaAs InAlP the epi peak separation. From Eq. 3.1 we estimate the required lattice− mismatch for growing a 530 nm thick InAlP layer, 3 free of threading dislocations, to < 0.5 10− . From Fig. 3.5 it is seen that the Al-content should be controlled to within× 0.2 % in order to achieve such low lattice mismatch. Since the InAlP is to be used as a sacriﬁcial layer we do not need to be concerned with the amount of threading dislocations, but it gives an idea of the lattice match needed in order to avoid strain eﬀects manifesting during growth. The growth of InAlP was found to be sensitive to the underlying structure with hillock formation (believed to be segregation of In) resulting from growth on rough surfaces.

52 CHAPTER 3. DEVICE FABRICATION

400 -1.50E-3

200 -0.75E-3 a/a

0 0.00E-3

-500 -250 0 250 500

-200 0.75E-3

Rel. Rock Angle ["]

T = 610 C

-400 1.50E-3 Latticemismatch, InAlP peakInAlP separation ["]

In Al P XRD -600 2.25E-3

1-x x

Linear Fit

48 50 52 54

Aluminum content, x [%]

Figure 3.5: Plot of the aluminum content, x, and epilayer peak separation for In1−xAlxP. The inset shows the relative intensity of the x-ray diﬀraction measurement versus rocking angle relative to the GaAs Bragg Angle θB,GaAs = 33.03.

3.2 Sacriﬁcial release etch

A critical process step is the sacrificial release of the mechanical structure, which forms the cavity air-gap. A sacrificial layer acts as a place-holder at the desired position of the air-gap during processing. At the end of the device processing the sacrificial layer is etched away, thus leaving behind the desired air-gap. This kind of semiconductor processing has been known for more than 50 years [21]. The sacrificial layer can either be deposited onto the epitaxial substrate or grown during the epitaxial process. The advantages of the first approach, which is well-established, is that the sacrificial layer can be deposited independently of the underlying substrate. The advantage of the monolithic sacrificial layer is that the layers above can maintain their crystal structure. This is important for applications where e.g. the piezo-electric properties depend on the zinc-blende crystal structure such as is the case for AlxGa1 xAs [86]. − 3.2.1 General considerations For devices based on GaAs substrates there is a large variety of ternary compounds that can be used for sacrificial etching [87]. Since we would like the thickness of the sacrificial layer to be a free parameter, the ternary compound must be lattice-matched to GaAs. The thickness required for Fabry-Pérot cavity devices range from around a fourth of the wavelength to one or more multiples. AlGaAs can be lattice-matched to GaAs over the entire composition range and is therefore widely used as sacrificial material [88]. Ga0.51In0.49P is also lattice- matched to GaAs and have been used for sacrificial etching, in particular where

53 CHAPTER 3. DEVICE FABRICATION

GaAs InGaAs AlGaAs InAlP GaInP AlOx C6H8O7:H2O2 E [93] CD [94] CD [95, 96] S S HCl:H2O S S CD [97] E [90] E [89] E HF:H2O S CD [98] E E NH4OH:H2O2 E CD [99] (E)

Table 3.1: Etchant selectivity for the materials present in the material system used for the HCG-VCSEL . E = Etches, CD = composition dependent, S = Slow (≈ 1-10 nm/min). an Al-free material system is desired [89]. The last candidate taking into account the lattice-match criteria is In0.49Al0.51P, which thus far has not been used for sacrifical etching to the authors knowledge [90]. Hydroflouric acid is favoured for etching of AlxGa1 xAs where x 0.5, showing high etch-rates and selectivities at the same time [88].− Hydrochloric≥ acid (HCl) has been reported for sacrificial wet etching of both In0.49Al0.51P and Ga0.51In0.49P selectively to GaAs[90, 91]. The good etching properties of both compounds in HCl is likely to be rooted in both AlCl3 and GaCl3 to be soluble in water. The greater affinity of AlCl3 to water, compared to GaCl3 might also account for the higher etch- rate of In0.49Al0.51P. The etch-rate of In0.49Al0.51P in concentrated 37% HCl is five times higher that that of Ga0.51In0.49P [92, 91]. The lateral etch-rate of Ga0.51In0.49P has been reported for different crystallographic orientation, while this is not the case for In0.49Al0.51P where only the bulk properties has been examined [89]. Selectivity to GaAs is of interest in VCSELs for 1060 nm and above, but at lower wavelengths such as 850 nm AlxGa1 x would be favoured due to its lower optical absorption compared to GaAs. Anhydrous− (water-free) citric acid (C6H8O7) mixed with hydrogen peroxide (H2O2) and ammonium hydrox- ide (NH4OH) has been used for etching of GaAs selectively to Al0.15Ga0.85As with selectivities up to 100[93]. Since we focus on 1060 nm VCSEL the use of citric acid is not an option. Tab. 3.1 summarizes the etch properties of selected binary and tenary semiconductor compounds, together with the oxide of aluminum, for different etchants. From the table it is seen that etching in HCl:H2O stops on GaAs, while both In0.49Al0.51P and Ga0.51In0.49P are etched. AlOx also etches in HCl:H2O, but with a selectivity of 1:50 towards InAlP. The metal stacks (Ti,Pt,Pd,Au) will not etch in HCl due to the lack of an oxidizing agent. Since HCl has been reported to show complete selectivity to GaAs it was chosen for further investigation [87].

3.2.2 InAlP sacriﬁcial etch

For this work we choose to focus our efforts on In0.49Al0.51P as sacrificial material given its high etch rate as compared to Ga0.51In0.49P. This is an advantage in the sacrificial release of "large" structures such as Fabry-Pérot filters where the minimum size is restricted by focusing of the optical beam spot size. In order to test the etching characteristics of InAlP using HCl, in particular the dependence on crystal direction, samples with GaAs/InAlP layers were masked with the positive UV-resist AZ5214E. The pattern was transferred to the GaAs using dry etching and the sample was then etched in HCl at differ-

54 CHAPTER 3. DEVICE FABRICATION

[011] [010] [011]

2 min HCl:2H O

15 min HCl:5H O

6 2

4 m/min]

2 Etch rate [ rate Etch

0 15 30 45 60 75 90

Angle [degrees]

Figure 3.6: Etch rate (µm/min) as a function of the crystal direction normal to the plane being etched. The graph shows the etch-rate for HCl diluted to water and 5 times water, respectively. ent concentrations. The etch rate in different directions was measured from 40 µm squares using differential contrast imaging (DIC) to see the undercut of the GaAs. The direction was measured relative to the major flat to which the pattern was aligned. This means that there is an uncertainty of around 3◦ on the direction with regards to the major crystal axis as given by the specifications on the GaAs wafer. Alignment to a cleaved flat or etched pits could remove this uncertainty.

3.2.3 Results

It has been found that the wet etching of In0.49Al0.51P in HCl:2H2O is limited by 111 planes that etch by 0.5 µm/min at 22◦C. The etch-profile is typical { } of anisotropic reaction-limited etching with a slope of 55◦ corresponding to the angle of the (111)¯ to the (100) surface. The observed crystallographic dependence match the expected behavior stopping at the column III-terminated (111) surfaces where the rate-limiting In/Al atom have 3 backbonds and 1 dangling bond. It is widely reported that HCl does not etch GaAs, since etching of GaAs is normally mediated by an oxidizing agent [90]. When using diluted HCl for etching, H2O can act as an oxidizing agent, forming Ga2O3, and although the oxidation rate is very low ( 0.5nm/hr for pure H2O) it can significantly increase when the pH-value of≈ the mixture is lowered[100]. This could explain the slow etch rate of 2 nm/min of GaAs in the [110]-direction by HCl:2H2O observed in device processing. Although this is 250 times slower than the etch rate of In0.49Al0.51P, the dimension of the HCG patterns etched in GaAs are also around 25 times smaller. Another concern is etching of Al-containing layers, in particular the oxidized AlGaAs. The reactive nature of aluminum makes it difficult to avoid any reaction, but one advantage is that the aluminum oxide is more resistant to wet

55 CHAPTER 3. DEVICE FABRICATION

30m m

Figure 3.7: Scanning electron micrograph (SEM) of cantilever beams released using HCl:2H2O and critical point drying. The beams are up to 350 µm long and 0.28µm thick. The beams to the right and left are 10 and 40 µm wide, respectively. The inset shows a free-hanging cantilever (the electrons are not reﬂected from the empty space underneath). The airgap is 0.5µm.

etching. Experiments where epitaxial layers of Al0.9GaAs were exposed show selectivity of 1:5 when compared with InAlP, while in the case of AlOx lateral etching of AlOx (sandwiched in between GaAs) was not observed. Fully exposed thin films of AlOx, on the other hand, showed a selectivity of 1:50. It has been reported that AlxGa1 xAs will be etched by conc. HCl for x 0.3[97]. Here − ≥ we have not seen etching of Al0.98GaAs in HCl:xH2O with x > 2 during device processing. This makes the use of Al0.51In0.49P viable as sacrificial material in device processing of AlGaAs-based 850 nm HCG-VCSELs. Fig. 3.7 shows a scanning electron micrograph (SEM) of fully released cantilevers. The sacrifical etching was done using HCl:2H2O and critical point drying. The slight curvature of the cantilever apparent in the inset could indicate either a difference in the surface properties of the top and bottom surface of the cantilever (leading to different water condensation behaviour) or that another material remains at the bottom surface. SEM of completely released HCG-VCSEL top mirrors (curled up due to the stress of the gold contacts) do not show any residues, why it is postulated that the slight bending is due to different surface wetting. The cantilever test structures are are an order of magnitude longer than the HCG VCSEL, where height measurement by confocal microscopy show perfect flatness.

3.3 Grating pattern transfer

Apart from the establishment of a process for the sacrificial release of III-V structures in GaAs, another focus of the process development has been the grating patterning. The following section will go through the results of the different mask and dry etching combinations to provide an overview on this part of the work. The first III-V dry etching process established at the cleanroom facility was RIE using flouroform (CHF3) and methane (CH4) for etching of silicon oxide (SiO2)/silicon nitride (Si3N4) and InP/GaAs, respectively [101, 102]. The RIE is equipped with an quartz carrier and this results in significant heating of the photoresist which lowers the etch resistance and especially in the case of

56 CHAPTER 3. DEVICE FABRICATION

Bias Flow Pressure Coil Platen Cl2 Ar [W] [W] [sccm] [sccm] [mTorr] 800 70 4 12 6

Table 3.2: ICP GaAs Nano etch

500nm 500nm

Figure 3.8: Scanning electron micrographs of the nano patterning left: after pattern transfer from the positive electron beam resist (ZEP520a) to the Si3N4 right: after sacriﬁcial etching.

ZEP520a compromise the resist structural stability [101]. During the project Inductively Coupled Plasma (ICP) was installed and the GaAs etching process was transferred from the RIE to the ICP. This meant an increase of the grating pattern etch rate from 9 to 160 nm/min. This is facilitated by the decoupling of the plasma generation and the substrate bias in the ICP allowing for very high powers to increase the radical density, while keeping both the pressure and substrate bias power low. In this way the etch-rate is signiﬁcantly increased without the physical etch increasing as would be the result of increasing the plasma density in a RIE system by increasing the substrate bias. Table 3.2 shows the etch recipe used for etching GaAs grating patterns. This etch was optimized for etching holes with vertical side-walls in GaAs photonic crystal structures. The etch-rate of GaAs was approximately 300 nm/min, but due to the aspect-ratio dependent etching (ARDE) eﬀect the etch-rate of the grating pattern was around a factor of two lower.

3.3.1 Si3N4 mask In the ﬁrst batches the e-beam resist ZEP520a was used to transfer the HCG pattern into a 180 nm Si3N4 hard mask, which was then used to transfer the pattern to the 0.28µm thick GaAs3. ZEP520a is a positive e-beam resist and thus only the air spacing of the HCG is written. The pattern transfer into Si3N4 after ZEP520a resist development was done by RIE. A CHF3/O2 dry etch was used at an etch rate of 17 nm/min. For the pattern transfer into GaAs a cyclic CH4/H2-based RIE with (CH2)x passivation and a oxygen plasma etch-back or a Cl2/Ar-based ICP was used [101]. For the CH4/H2 RIE, the etch-rate of the grating structures was 9 nm/min, while it was 38 nm/min in larger areas, and

3The reason for using silicon nitride instead of silicon oxide was that a better selectivity to ZEP520a has been reported [101]

57 CHAPTER 3. DEVICE FABRICATION

328nm

126nm 500nm 200nm

Figure 3.9: Scanning electron micrographs of the nano patterning left: before the positive electron beam resist (ZEP520a) has been removed and right: after the resist has been removed on the full epi-structure.

the selectivity Si3N4:GaAs was 1:4 [102, 101]. The substrate was placed on a built-in quartz carrier with no active temperature control. The lack of substrate cooling means that the resist is heated during etching, which results in poor etch resistance (the selectivity being 1:1). Mask erosion during the long etches required to transfer the nanometer pattern into Si3N4 resulted in severe linewidth broadening on the order of 70 nm for 18 min etching. The linewidth broadening observed could be a combined effect of ZEP520a contraction due to charging and temperature effects together with mask erosion at the edges due to the physical component of the etch. Resist residues was observed to be a problem. This leftover resist at the bottom would negatively affect the pattern fidelity by blocking the etch of the GaAs[101]. The linewidth broadening could only be partly accountedfor by a linewidth reduction during e-beam writing. The reason is that the 600-nm thick ZEP520a, required to withstand the duration of the etch, also means significant forward scattering during e-beam writing, which limited the minium linewidth in the ZEP520a to around 40 nm. This makes the aspect ratio of the ZEP lines around 1:15, which helps to explain the factor of 2 in RIE lag encountered. In addition the sidewall curvature tampered the following pattern transfer. Opening up for fluoride-based etching on the ICP would make it interesting to use it for transferring the nano-sized patterns from the ZEP520a into a SiO2 or Si3N4 hard mask allowing for much deeper etching. The selectivity of Si3N4:GaAs was found to be better than 1:10 for etching in the ICP.

3.3.2 ZEP mask

In order to overcome the limitations of the RIE etching of Si3N4, eﬀorts were made to use ZEP520a directly on GaAs as enabled by ICP etching. The higher etch rates enabled by the high radicals density in ICP at lower platen power allowed ZEP520a to be used to transfer the pattern. The GaAs etch-rate was 300 nm/min with the etch-rate of the grating patterns being 160 nm/min and the ZEP520a:GaAs selectivity being 1:1. Due to the poor adhesion of ZEP520a on GaAs a thin SiO2 adhesion layer was deposited before spinning ZEP520a. Fig. 3.9 shows the cross-section of part of the HCG before and after removal of the ZEP520a mask. In the left scanning electron micrograph (SEM) mask

58 CHAPTER 3. DEVICE FABRICATION

331nm 129nm

200nm 200nm

Figure 3.10: Scanning electron micrographs of the nano patterning after the negative electron beam resist (XR1541) has been removed left: in cross-section right: from above. erosion of the ZEP520a is clearly visible. Before dry etching the ZEP520a sidewalls are vertical, but after dry etching they are slanted4. This is believed to be due to the strong physical component of the etch. The right picture in Fig. 3.9 shows the a topview of the HCG after the sacriﬁcal etching. The GaAs sidewalls are perfectly vertical and the line edge rougness is very low. For too long etch duration it was seen that mask erosion would be transferred into the resist. This hindered long over-etching to ensure that the InAlP was reached. The selectivity between GaAs and InAlP was 1:3 - the lower etch rate of InAlP likely due to the low volatility of InCl3 at the etch temperature of 20◦. The InAlP is later fully removed, why overetching is not a problem in that regard. In order to increase the etch depth of GaAs, the selectivity should be improved by optimizing the etch in terms of pressure, platen and coil power. Another possibly simpler route is to simply decrease the platen temperature in order to reduce the heating of the ZEP resist5.

3.3.3 HSQ mask For the HCG-VCSELs it was decided to use the negative e-beam resist hydrogen silsesqouioxane (HSQ). The negative resist HSQ can be cured into SiO2 and thus should show good etch resistance during pattern transfer. Furthermore it is generally found that a hard mask, in the form of an oxide or nitride, yield a lower line-edge roughness compared to e.g. metals or photoresists. The smaller dimensions of the HCG both required better alignment of the grating to the mirror and allowed for shorter writing times. The big metal pads was written with a high current of 64 nA which was overlaid the grating pattern written by 10 nA. The selectivity of GaAs:HSQ was expected to be better than 1:10 but was found to be less than 1:7. A lower etch resistance of HSQ than SiO2 is also

4This is partly an artefact of SEM imaging. The heating induced will make the ZEP contract, which was conﬁrmed by changing the exposure time in cross-sectional imaging. The kink in the resist is though believed to be related to the dry etch 5Heat transport from the sample to the carrier substrate was found to be very impor- TM tant and to that aim Crystal Bond was used to improve heat transfer. Applying Crystal TM Bond meant the diﬀerence between fully burned ZEP (and thus failed dry etch process) or successfull pattern transfer.

59 CHAPTER 3. DEVICE FABRICATION what is reported elsewhere [103]. The selectivity is still much better than that of ZEP:GaAs and it should be adquate with a 100-nm HSQ mask in order to etch 350 nm GaAs. The results of etching GaAs with a 180 10 nm HSQ mask is seen in Fig. 3.10. Smooth sidewalls result and the design± duty cycle of 0.72 was achieved. Mask erosion was found to be a problem in obtaining smooth sidewalls, resulting in sidewall roughness on the order of 5-20 nm. The mask erosion was found to both depend on the HSQ exposure dose and development conditions. It has been observed that thick HSQ is necessary to avoid mask erosion being transferred to the substrate in etching GaAs[103]. Increasing the resist thickness presents a trade-oﬀ since as the etch rate decreases the mask will be exposed to the same amount of erosion given the longer etching time that will be necessary to reach the same depth. Increasing the resist contrast by decreasing the soft bake temperature was found to decrease the mask erosion and this can be attributed to better curing of the resist (e.g. easier removal of non-cured resist).

3.4 HCG Fabry-Pérot ﬁlter

The starting epitaxial substrate for the HCG Fabry-Pérot filter fabrication consist of an n-doped DBR, Al0.49In0.51P sacrificial layer and an n-doped GaAs HCG layer. Following the HCG pattern definition, the full mirror structure with bonding pads was transferred into the GaAs layer using positive AZ5214E resist lithography exposed by ultra-violet (UV) light. The alignment accuracy was within 1 µm on a quarter 2 inch sample. The top metal NiGeAu n-contact was patterned by lift-off lithography using a bi-layer resist scheme with 600-nm AZ5206 on 500-nm LOR5B. The LOR lift-off resist is stated not to scum, but a descum for 1 min in an oxygen plasma was found to be required 6. The backside of the substrate was then polished using Chemlox (sodium hypochlorite) with a Chemcloth polishing pad in order to achieve a smooth surface, hence reducing light scattering at the interface. The backside was further coated with an anti-reflective coating (ARC) - either SiO2 or SiO2/TiO2. The backside must be protected with photoresist during sacrificial release, since it was found that the ARC disintegrate. The NiGeAu n-contact was alloyed using rapid thermal annealing at 420 ◦C for 10 seconds[104]. The last step was the sacrificial etching of the InAlP to define the air-gap with critical point drying to avoid stiction.

3.5 VCSEL processing

Standard oxide confined VCSELs with n- and p-doped DBRs were processed in order to benchmark the InGaAs MQW. In the first photolithographic step AZ5214E is used as a hard-baked mask to wet etch the oxidation mesas using 1H3PO4:4H2O2:45H2O. In order to improve the adhesion of the photoresist, a 100 nm thick SiO2 layer is first deposited by PECVD in order to take advantage of the superior adhesion of AZ5214E to HMDS treated SiO2. After the mesa etching the Al0.98Ga0.02As oxidation layer is oxidized by 440◦C wet oxidation. The aim was to oxidize to a 5-µm oxide aperture. The oxidation process requires

6 Scum refers to insoluble resist left after development. This is often removed with O2 plasma ashing, which is also referred to as descumming.

60 CHAPTER 3. DEVICE FABRICATION very good uniformity and composition control of the AlGaAs layer which was not established at the time of writing. This means that the oxidation rate varies widely across the wafer due to differences in Al-content [84]. Just before oxidation the oxide adhesion layer is wet etched in buffered hydroflouric acid (BHF) in order to avoid it covering the oxidation layer. After wet oxidation the surface is coated with SiO2 and planarized using BCB. The BCB is etched back, after hard-curing, using O2/CHF3 based RIE at an etch rate of 140 nm/min. End-point detection is used to stop at the SiO2 which functions as the isolator beneath the top diode contact. An opening is made in the SiO2 on the mesa by BHF wet etching and a Ti/Pt/Au metal stack patterned by lift-off using a bi-layer resist scheme. In order to improve the formation of an ohmic contact deoxidation of the surface is done using HCl:H2O. In the same manner the backside is deoxidized and degreased in NH4OH:10H2O, with the frontside being covered by hard-baked AZ5214E photoresist7. This is then followed by blanket deposition of an Ni/Ge/Au metal stack. The last step is a rapid thermal alloying at 420◦C for 10 s to form ohmic contacts.

3.6 HCG-VCSEL processing

The starting substrate for the HCG-VCSEL processing is covered in Sec. 3.1.2. Due to the much smaller mirror dimension for the HCG-VCSEL the HCG and mirror layout, including contact pad, was patterned in a single step using the negative resist HSQ. Figure 3.11 shows SEM of HCG before sacrificial etching. The left SEM shows that good pattern fidelity has been achieved. The right SEM shows a tilted view of the grating with the HSQ still on top. Limited sidewalls roughness is seen. The exact same parameters as in Fig. 3.10 was used and the difference in sidewall roughness shows that the process is not completely stable. In the next step the p-doped GaAs is reached by wet etching using positive UV lithography (the resist protecting the HCG). This is then followed by pattern definition of the oxidation mesa using wet etching - again with positive UV lithography. This step also defines the contact mesa for the p-contact. To confine the current to the same area as the HCG and to ensure single-mode lasing, an oxide aperture is defined by oxidation of an Al0.98GaAs layer in a

7 This step is not necessary in the case that the sample is lapped down in AlOx

Figure 3.11: SEM of the left: HCG of the VCSEL and right: close-up on the HCG ◦ grating. The wafer is tilted 15 to show the sidewall roughness. The HSQ mask has not been fully removed and is seen as a thin layer on top of the grating bars.

61 CHAPTER 3. DEVICE FABRICATION

10mm

Figure 3.12: Plot of the PL peak and FWHM of the processed HCG-VCSEL after wet oxidation.

steam ambient furnace at 440◦C. Figure 3.12 shows the PL peak and FWHM of the fourth quater after the wet oxidation. The median peak wavelength is 1048 nm with a 19 nm FWHM. This is a 10 nm blue-shift relative to the test MQW growth. An explanation of this blue-shift (apart from simple reactor drift) could be quantum well intermixing during the growth of the AlGaAs oxidation layers, which is done at 720◦. The PdGeTiPtAu top contact is patterned using lift-off with image reversal of AZ5214E after which the NiGeAu backside contact is deposited. In order to simplify the contact lithography the same metal stack has been used for both the top MEMS n-type and laser diode p-type layers [105]. The contacts are alloyed in a single step rapid thermal annealing at 420◦C for 15 s. After alloying the contacts the air-gap is defined by sacrificial etching of the InAlP using critical point drying to avoid stiction.

3.7 Summary

Process flows for the realization of electro-static tunable HCG Fabry-Pérot filters and HCG VCSELs have been developed. This has involved work on all aspects of the process, from epitaxial growth to sacrificial wet etching. MOVPE growth of 1060 nm MQW In0.3Ga0.7As active material with strain balancing has been developed. Good material quality has been achieved with the In- GaAs/GaAsP MQW showing well-defined x-ray diffraction superlattice peaks with 120" FWHM and photoluminesence with 20 nm FWHM. Furthermore growth of lattice matched InAlP has been characterized together with the crystallographic dependence of the etchrate in diluted HCl. Based on the MOVPE grown laser material standard oxide apertured VCSEL with 25/35 top/bottom DBR pairs have been fabricated and tested. A large part of the process development has also been the investigation of different mask and dry etch techniques to transfer nanometer patterns defined in e-beam resist. The best results have been achieved by transferring the pattern of the e-beam resist HSQ directly to GaAs by ICP etching. In general it is noted that mask erosion is an issue in transfering patterns with a critical dimension < 100 nm. Based on the In- AlP sacrificial etch and nanopatterning, HCG VCSEL have been fabricated and tested.

62 Chapter 4

Fabry-Pérot ﬁlter results

In this chapter the results on the Fabry-Pérot filters are presented. Fabry- Pérot filters based on AlGaAs/GaAs epitaxy was demonstrated in 1995 with a relative tuning range of 7.5% at moderate voltages [57, 106]. Large-signal modulation at frequencies up to 150 kHz have been demonstrated using a DBR pillar as the top mirror, which decouples the reflectivity from the mechanical design [70]. Few examples exist in literature on Fabry-Pérot filters with high- index contrast subwavelength gratings. From a conceptual point of view the ideal structure would consist of a Fabry-Pérot cavity with two HCG mirrors. This would ensure a high finesse, low transmission loss Fabry-Pérot filter. HCG Fabry-Pérot filters has been demonstrated in the AlGaAs/GaAs system with a Q-factor of 40 for an air-gap cavity [107]. Similar finesse has been demonstrated in the AlGaAs/GaAs system with a top HCG mirror and bottom DBR mirror sandwiching an oxide cavity [108]. A Q-factor of 1047 has been demonstrated in the InP/InGaAs system with a top HCG mirror and bottom InP/air DBR with an air-gap cavity [109]. The latter work demonstrates that high finesse can be achieved with a HCG-DBR Fabry-Pérot filter. The structure pursued here is similar to that of [109] et. al. with the difference that a solid bottom DBR is used.

4.1 Transmission measurements

The filters are intented for use as transmissive filter and has been tested as such. The characterization of the filter was done by using a white-light source and a Optical Spectrum Analyzer (OSA) to look at the transmission spectrum. The HCG is highly polarization dependent and therefore the polarization state of the input light was made linearly polarized.

4.1.1 Fiber-based setup

TM The transmission measurement setup consists of the following: a SuperK white-light source, a Glan-Thompson polarizer prism, a Neutral Density (ND) filter, a Polarization Maintaining (PM) fiber and a multimode (MM) fiber. The spectrum was measured using an OSA. The SuperK supercontinuum laser light source covers the full range of interest with the major drawback that the light

63 CHAPTER 4. FABRY-PÉROT FILTER RESULTS

OSA Whitelightsource

MMFiber PMFiber Polarizer

FabryPérotFilter NDFilter

Figure 4.1: Sketch of the experimental setup used to characterize the Fabry-Pérot filter transmission. A polarizer controls the polarization state of the light which is coupled into a polarization maintaining fiber after attenuation. is generated by a 1064 nm laser, which thus shows up as an artefact in the spectrum. The extinction ratio of the polarizer prism was found to be 13 dB measured by a power meter. The stress-rods of the fiber were misaligned 45◦ to the turn key, which has been accounted for in reading off the polarization∼ angle from the polarizer prism. A 10 dB ND filter was used to lower the high output power from the light source (100 mW) which would otherwise melt GaAs1. The PM fiber was a photonic crystal fiber (PCF) with a large mode diameter of 9 µm. Assuming a Gaussian beam, the beam waist would be 13 µm for a propagation distance of 250 µm, which is smaller than the minimum mirror sidelength of 20 µm. In order to provide an absolute measure of the transmission, a reference measurement was done each time at the same distance between the 62.5 µm MM and 9µm PM fibers, as for the device measurements. Hence, the free-space loss due to the beam divergence is accounted for in the results as presented here. In order to align the PM fiber to the HCG, two microscopes were used. The sample was placed vertical to allow for easy coupling to the two fibers. One microscope allowed for a sideview of the sample, the slight tilting of which allowed to see the top metal contact. In this way the fiber could be aligned in one direction. For the other direction a microscope was placed to see the sample surface at an angle. In this way the spot could be seen on the sample.

4.1.2 Filter transmission Fig. 4.2 shows the measured transmission spectrum of a Fabry-Pérot filter with 20 µm grating area for both TE and TM polarization (with respect to the grating direction). The spectrum for TE polarized light compares well qualitatively to the 30 pair n-DBR transmittance spectrum. The minimum transmittance 1 of -30 dB is higher than the theoretically expected -34 dB assuming 5 cm− 18 3 loss at a Si doping concentration of 10 cm− . In order to match the measured 1 transmittance the loss should be 20 cm− or equivalently a Si doping concen- 18 3 tration of 4 10 cm− . The measured transmission is close to the noise floor of the OSA× why this is subject to some uncertainty. For TM polarization a peak transmission is seen inside the DBR stopband at 1027 nm with a FWHM of 4.4 nm. This makes the Q-factor of the filter 233. The difference between the transmission of the TM and TE polarized light is seen to be around 10 dB. A higher ratio would be expected, but to resolve this a polariser prism with a

1Luckily the amount of arsine that could escape is minute, but the device will nevertheless not survive

64 CHAPTER 4. FABRY-PÉROT FILTER RESULTS

-5

-10 = 1027 nm

= 4.4 nm 10.7 dB

FW HM

-15

-20 Transmittance[dBm]

-25

TM -30

-35

950 1000 1050 1100 1150

W avelength [nm]

Figure 4.2: Plot of the filter transmission spectrum for a 20 µm HCG grating filter. larger extinction ratio must be used. The reduction in transmission can arise from a high HCG reflectance, absorption loss or diffraction into higher order modes than the zeroth.

4.2 Discussion

HCG Fabry-Pérot filters have been fabricated and their transmission spectrum measured. Q-factor of around 200 has been measured, far short of the 15000 expected for such high-reflectivity mirrors. An explanation to the mismatch between the measured and expected Q-factor can be found in the analysis of Sec. 2.3 from which it was found that both the filter linewidth and transmission loss increases with decreasing mirror reflectance. Another source of optical loss, which would also degrade the Q-factor, would be beam walk-off. This beam walk-off effect on the optical Q-factor will depend on the mirror reflectance. An simpler method of measurering the HCG reflectance is warranted, e.g. measuring the reflectance of an oxide-gap HCG.

65 Chapter 5

VCSEL results

In this chapter we report on the results of the fabrication of 1060 nm VCSELs, which is presented in Sec. 5.2. A standard VCSEL structure with a semiconductor λ0 cavity, top and bottom DBRs was made in order to test the gain material grown. Section 5.3 describes the characterization of a HCG VCSEL with a λ0/2 air-gap and an air-clad HCG. Light-Current-Voltage (LIV) characterization was done for both VCSELs, and for the HCG VCSEL the MOEMS tuning was further tested. The measurements are the ﬁrst for a HCG VCSEL with no p-doped top DBR mirrors.

5.1 Experimental setup

In order to measure the opto-electrical characteristics of the VCSELs fabricated a standard probe station setup was used. Needle probes were used for making electrical contact to the MEMS contact pad and the VCSEL p-contact pad. The VCSEL forward current was controlled by a laser driver (ILX LDC-3724) at constant current. The p-contact was used as the MEMS gnd contact to apply a positive floating potential difference to the MEMS contact using a DC Source Measurement Unit (HP6632A) or a Keithley High Current Source Measure Unit (238). For dynamic operation a Arbitrary Function Generator (HP33120a) was used with a +/- 15V amplifier and bias tee to set a DC offset to the AC signal. The output power was measured using a large-area Si photodiode (Thorlabs

OSA SMFiberProbe + LaserDriver

V,ILD - VCSEL Cumount Peltierelement

Figure 5.1: Sketch of the experimental setup used to characterize the VCSELs

66 CHAPTER 5. VCSEL RESULTS

FDS1010) with a responsivity of 0.6-0.2 A/W at 1000-1100 nm. The output power stated here are calculatedR using the responsivity data given by the manufacturer1. The uncertainty on the output power is < 15%. The optical spectrum of the VCSELs was measured using a standard Single Mode (SM) telecom fiber (SMF-28) to collect the light. A peltier element together with a standard thermistor was used for temperature control of the sample holder. A sketch of the setup is seen in Fig. 5.1. The fiber probe was placed in close viscinity to the VCSEL using a power meter for optimizing the signal and a monitor to visually control the distance of the fiber to the sample.

5.2 VCSEL

5.2.1 Device structure

The epitaxial structure was designed as a λ0 cavity with 25 and 35 pair top and bottom DBRs. The mirrors were doped to a constant level of approxi- 18 3 mately 2 10 cm− . In the ﬁrst layer of the top DBR, the Al-content was increased× to 98% such as to be oxidized to be the current aperture later on. The λ0-cavity consisted of undoped GaAs cladding on both sides of the 3 MQW In0.3Ga0.7As/GaAs0.8P0.2. In order to be able to make ohmic contact to the top DBR the temperature was decreased to 580◦C during the growth of the top 19 3 GaAs layer. This should increase the doping concentration to 4 10 cm− allowing thermionic current transport. ×

5.2.2 Laser characterization The fabricated VCSELs were tested in terms of their optical spectrum and LIV characteristics. Fig. 5.2 shows the optical spectrum of a SM VCSEL at 1.5 to 3 times the threshold current of Ith = 4 mA. The optical spectrum was measured using a SM ﬁber to collect the light. The SMSR is 24 dB at 1.5Ith and remains

1http://www.thorlabs.com/images/TabImages/FDS1010-CAL_xls.xls

Layer Material Periods Thickness nL Function # [nm] λ0 12 GaAs:C 1 76.0 0.250 DBR/Contact 11 Al0.9GaAs:C 24 88.0 0.250 DBR low 10 GaAs:C 24 75.9 0.250 DBR high 9 AlOx/Al0.98GaAs:C 1 89.0 0.250 Oxide aperture 8 GaAs 1 109.3 0.360 Cladding 7 GaAsP0.2 3 11.0 0.035 Barrier 6 In0.3GaAs 3 8.0 0.026 QW 5 GaAsP0.2 3 11.0 0.035 Barrier 4 GaAs 1 33.4 0.110 Cladding 3 GaAs:Si 35 75.9 1.670 DBR high 2 Al0.9GaAs:Si 35 88.1 DBR low 1 GaAs:Si 1 Substrate

Table 5.1: Device structure of the VCSEL.

67 CHAPTER 5. VCSEL RESULTS

13 dB up to 20 mA. The lasing wavelength of 1056.5 nm is very close to the center photoluminescence wavelength of 1063 nm from the calibration epitaxial MQW growth (see Fig. 3.2). This indicates very good control of the cavity growth. The wavelength dependence on driving current is 0.25 nm/mA. The laser linewidth was more narrow than the limit of 0.1 Å on the spectrometer. Fig. 5.3 shows the LIV characteristic of a SM VCSEL. From Fig. 5.3 it is seen that the differential quantum efficiency is very low, around 1%. For the given design with 35 pair bottom DBRs and only 25 top DBRs all the power will be coupled out the top mirror, but due to the high loss of the p-doped top mirror only 43% will be coupled out. The mirror transmission loss can be estimated 1 from TMM to be 19 cm− when the loss of the mirror is included in the total cavity loss αi . Then assuming a quantum efficieny, ηi, of 0.8 the total internal loss can beh estimatedi to be

(F1ηi ηd,1) αm 1 αi = − = 46.4 cm− . (5.1) h i ηd,1

For a VCSEL the transverse confinement factor is close to unity since the optical field and the electrons are both confined by the oxide aperture. The axial confinement factor for this epi-design is Γz = 0.0347 and thus the threshold 1 gain can be estimated to be 1888 cm− . Assuming that the optical loss of the top p-doped DBR is 30/cm the reflectance would be 99.8%. Fig. 5.4 shows LI curves for a MM device at different substrate temperatures. The VCSEL substrate temperature was controlled through a peltier thermoelectric cooler. The characteristic temperature is 200 K.

68 CHAPTER 5. VCSEL RESULTS

-40

9.5mA 9.0mA -50

8.5mA 8.0mA 7.5mA -60 7.0mA 6.5mA 6.0mA

Rel.[dBm] Intensity -70

9.5mA-80 9.0mA 8.5mA 8.0mA 7.5mA 7.0mA 6.5mA 6.0mA 1056.0 1056.5 1057.0 1057.5 1058.0 1058.5 Wavelength [nm]

Figure 5.2: Plot of the optical spectrum of a oxide conﬁned 1060 nm VCSEL (OSA resolution 0.05 nm).

0.30 5

0.25 4

0.20 [mW]Power

3 0.15 Voltage[V] 2 0.10 V = 1.15 V I = 4 mA 1 th 0.05 P = 0.3 mW max

0 0.00 0 5 10 15 20 25 30 35 40 Current [mA]

Figure 5.3: Plot of the LIV characteristics of the 1060 nm oxide conﬁned VCSEL.

69 CHAPTER 5. VCSEL RESULTS

0.6 10 oC 20 oC 0.5 30 oC 40 oC o 0.4 50 C 60 oC 70 oC 0.3 Power[mW]

0.2

0.1

0.0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 Current [mA]

Figure 5.4: Plot of the light-current characteristics at diﬀerent temperatures of the thermo-electric cooler controlling the VCSEL substrate temperature.

5.2.3 Discussion The fabrication and characterization of the 1060 nm VCSELs show that single- mode laser can be fabricated based on the In0.3Ga0.7As/GaAs0.8P0.2 active material. The treshold current is high compared to the state-of-the-art [77]. The high threshold current could be due to optical absorption loss in the p- DBR. The low turn-on voltage and diode IV-characteristics indicate that the problem is not the DBR series resistance. Reducing the optical absorption loss, higher output powers and lower threshold currents would be expected.

70 CHAPTER 5. VCSEL RESULTS

5.3 HCG VCSEL

Since the HCG VCSEL was introduced by Huang et. al it has recieved increasing attention [19]. The major advantage of the HCG is that the requirements to epitaxial growth is relaxed. The first use of a HCG as part of a VCSEL demonstrated its use in reducing the number of top p-doped DBR mirror pairs [19]. Later demonstrations has shown that a HCG suspended on an oxide can fully replace the top p-doped DBR [49, 110]. We present for the first time that the ultra-high reflectivities (> 99.5%) required for lasing in a VCSEL can be achieved using an air-cladded HCG. Hence this is the first demonstration where the top reflector has been replaced by a single HCG. The major challenges in achieving lasing HCG VCSELs has been to achieve ultra-high reflectivity of the top HCG mirror and reducing optical loss due to the oxide aperture area exceeding that of the top HCG mirror.

5.3.1 Device structure The HCG VCSEL was designed to have an extended cavity using an anti- reflecting coating between the air-gap and semiconductor cavity. The device design is seen in Tab. 5.2 which shows the different material layers, their number of repetitions, thickness, optical thickness and function. The materials are read left to right and the dopants are written after a colon (:). The number of periods should be understood such that the layers with the same number are grown subsequently and the whole sequency repeated # times. The effective optical thickness are written for all layers that are part of the optical cavity. The cavity is designed as an extended cavity by supressing the reflections at the semiconductor-air interface. The bottom DBR has been doped to a Si concen- 18 3 tration of 1 10 cm− in order to lower the resistance. Since top emission is desired a high× number of bottom mirror pairs have been chosen. The number of pairs could be further increased, but the reflectance will not increase much further due to free-carrier absorption. In order to limit non-radiative recom-

Layer Material Periods Thickness nL Function # [nm] λ0 13 GaAs:Si 1 280.0 0.552 HCG 12 In0.48AlP/Air 1 484.9 0.457 Tuning gap 11 AlOx 1 171.0 0.250 AR-coating 10 GaAs:C 1 201.3 0.971 Current spreading 9 AlOx/Al0.98GaAs:C 1 55.0 0.154 Oxide aperture 8 GaAs 1 159.0 0.524 Cladding 7 GaAsP0.2 3 11.0 0.035 Barrier 6 In0.3GaAs 3 8.0 0.026 QW 5 GaAsP0.2 3 11.0 0.035 Barrier 4 GaAs 1 43.9 0.145 Cladding 3 GaAs:Si 35 75.9 1.670 DBR high 2 Al0.9GaAs:Si 35 88.1 DBR low 1 GaAs:Si 1 Substrate

Table 5.2: Device structure of the HCG VCSEL.

71 CHAPTER 5. VCSEL RESULTS

1 4 13 10 8 4 2-3

5-7

0.5 2 11

RefractiveIndex 12

ElectricFieldMagnitude(au.)

0 0 0 0.5 1 1.5 2 z-axis[ mm]

Figure 5.5: Plot of the electric field magnitude and refractive index of the HCG VCSEL. Details on the layers can be found in Tab. 5.2. bination, the cladding is undoped. The InGaAs MQW has been aligned to the fundamental of the mode field anti-node as seen in Fig. 5.5. The electric field profile has been calculated by CAMFR as covered in Sec. 2.4. The oxide aperture has been placed at a field anti-node in order to minimize the threshold material gain. From 3D FDTD simulation the HCG VCSEL is found to be single-mode for an oxide aperture of 8 µm. The confinement factor for this 1 design is Γ = 3.15% and the threshold material gain gth = 531 cm− . The FSR is 109 nm and the electro-static tuning range is found to be 30 nm at a tuning efficiency of 0.183 found from CAMFR simulations (the tuning efficiency from Eq. (2.31) is 0.209). The simulations are done for a λ0/2-cavity as seen in Tab. 5.2. As the air-gap only makes up a small part of the total effective cavity length of 4.85λ0 the decrease in tuning efficiency will be negligible, while the electro-mechanical tuning range will double from increasing the air-gap to λ0. The electro-static force on the other hand will decrease by one fourth, why a larger voltage will be required to cover the full tuning range.

5.3.2 Laser characterization The fabricated HCG VCSELs were tested in terms of their LIV characteristics and their optical spectrum as a function of both temperature and laser forward current. Here we show results for a single-mode HCG VCSEL with a 8.5 µm aperture. Fig. 5.6 shows LIV characteristics of a HCG VCSEL. The turn-on voltage, Von, is 1.8 V and the series resistance 210 Ω. The threshold current, Ith, of the device is 0.65 mA and the slope efficiency 0.15W/A. This is equivalent to a differential quantum efficiency of 13%. The maximum output power at 25◦C

72 CHAPTER 5. VCSEL RESULTS

5 1.0

Voltage

15 C

20 C

4 0.8

25 C

30 C

40 C

50 C 3 0.6

60 C

2 0.4 Voltage(V) Power (mW)

1 0.2

0 0.0

0 2 4 6 8 10 12

Current (mA)

Figure 5.6: Plot of the LIV characteristics of a SM HCG-VCSEL with Ith = 0.65 mA, Rs = 210 Ω and Von = 1.8V. The peak wavelength is λp = 1068 nm and the SMSR 45 dB. is 0.74 mW with a laser forward current of 9.5 mA. The laser was not cooled to more than 15◦ due to the risk of water condensation, which would cause stiction of the HCG. From Fig. 5.6 it is seen that the threshold current continues to decrease when lowering the temperature. The median photoluminescene of the MQW is around 1045 nm and thus the cavity peak of the VCSEL in Fig. 5.6 is detuned by 23 nm from the gain peak. Fig. 5.7 shows the spectrum of a HCG VCSEL versus current. The HCG VCSEL shows a high SMSR of over 40 dB across from 3 mA to 9 mA. Hence the laser remains single-mode up until the maximum output power. The wavelength dependence on current and temperature was found to be 0.33 nm/mA and 0.07 nm/K, respectively. From this it follows that the heating of the active region is 4.7 K/mA.

5.3.3 Static wavelength tuning

The static tuning range was tested by applying a electrical potential, vDC, between the contact to the HCG layer and the laser diode p-contact. The optical spectrum has been measured using, an optical spectrum analyzer, by coupling the VCSEL output into a single-mode ﬁber. Fig. 5.8 shows a plot of the optical spectrum (left axis) for diﬀerent voltages (right axis, open circles). The wavelength changes from an initial value of 1069 nm at 0V to 1053 nm at 35V, which is a total change of 16 nm. The change in peak intensity from 1069 nm to 1058 nm is less than 3dB, at which points it decreases abruptly. Hence the 3dB tuning range is 11 nm. Further electro-static tuning is limited by the pull-in instability and for this HCG VCSEL the pull-in voltage is close to VPI = 35V. The ARC protects the pin-junction from the high MEMS voltages and thus the

73 CHAPTER 5. VCSEL RESULTS

-30 9 mA 8 mA 7 mA -40 6 mA 5 mA -50 4 mA 3 mA -60 2 mA Intensity [dBm] Intensity 1 mA -70

-80

1066 1068 1070 1072 1074 1076 1078 1080 1082 1084 Wavelength [nm]

Figure 5.7: Plot of the optical spectrum of a SM HCG VCSEL. The SMSR remains more than 40 dB from 3 to 9 mA laser forward current. laser should be robust against pull-in. For a HCG VCSEL with an initial emission wavelength of 1070 nm we observe lasing at 1060 nm in the pull-in state with a 5 dB higher peak intensity.

5.3.4 Swept wavelength tuning The dynamic tuning range was tested by applying an alternating voltage v with a constant potential diﬀerence oﬀset of vDC overlaid with a sinusoidal with a peak-to-peak voltage of Vpp. Hence the MEMS voltage is of the form

v(t) = vDC + vAC cos (ωt) , (5.2) where ω is the angular frequency. In Fig. 5.9 the tuning amplitude is plotted versus excitation frequency f = 2πω for vDC = 6V and vAC = 1.5V. The plot shows that the HCG VCSEL tuning rate is limited by low-pass behavior - as was shown in Eq. (2.49). The amplitude peaks at 850 kHz and the quality factor Q of the mechanical resonator is found to be 4. The low quality factor is due to squezed ﬁlm damping. Because the excitation force, Fel, of the mechanical resonator depends on the square of the voltage as given in Eq. (5.2) it follows that v2 v2 F v2 = v2 + AC + AC cos (2ωt))+2v v cos (ωt) . (5.3) el ∝ DC 2 2 DC AC Hence as seen in Eq. (5.3) when driving the HCG VCSEL with an oﬀset al- 2 2 vAC ternating voltage it is in fact seeing a constant term vDC + 2 , an excitation

74 CHAPTER 5. VCSEL RESULTS

10 nm

-20 35

I = 5 mA

-30

TEC = 25 C

-40

-50

10 voltageMEMS (V) Relative(dBm)Intensity

-60

-70 0

1050 1055 1060 1065 1070

W avelength (nm)

Figure 5.8: Plot of the optical spectrum (left axis) and MEMS voltage (right axis) versus wavelength. at the angular frequency ω of the alternating voltage and a third term which will be referred to as the second harmonic excitation at 2ω. In order to suppress the second harmonic excitation vDC >> vAC. Fig. 5.10 shows the optical spectrum without excitation (solid) and for a resonant excitation with constant oﬀset vDC = 10V and vAC = 5V (dashed) and vAC = 3.5V (dotted). The optical spectrum of the swept HCG VCSEL is an integration of the instantenous peak intensity as the OSA acquisition time is much shorter than the tuning rate. The shape of the optical spectrum is characteristics for a sinusoidal displacement for which we expect the spectral density to diverge at the edges of the tuning range [72]. Since the electro-static actuator is driven to a forced oscillation the tuning can extend to both sides of the initial peak wavelength. This enables a tuning range that is potentially twice that of the static tuning range. From Fig. 5.8 the static 3dB tuning range was found to be 11 nm compared to the resonant tuning range of 23 nm.

5.3.5 Mechanical characterization The mechanical spectrum was measured using a laser Doppler vibrometer (Poly- tec MSA-500). Figure 5.11a shows the mechanical spectrum, measured in partial vacuum with no applied excitation, from which the resonance frequency is determined to be 820 kHz and the mechanical Q-factor 3774. Since there is no external force applied and the mechanical frequency is far from any naturally occuring vibrations it must be due to thermal vibration. By scanning the laser beam, piezoelectric wideband actuation, across the HCG and spring suspension the mode shape was conﬁrmed to be that of the fundamental mode (see Fig.

75 CHAPTER 5. VCSEL RESULTS

V = 6V V = 3V

DC pp

f = 850 kHz

res

1 Sweepamplitude (nm)

0.1

3 4 5 6

10 10 10 10

Frequency (Hz)

Figure 5.9: Plot of the sweep amplitude (peak wavelength envelope) versus frequency. .

Resonant 10 Vpp

Resonant 7 Vpp

-20

Static

-30

23 nm

-40

-50

-60 Relative[dBm] Intensity

-70

-80

1050 1055 1060 1065 1070 1075 1080 1085

W avelength [nm]

Figure 5.10: Plot of peak wavelength envelope at VDC = 0V (dashed) and at a small- signal tuning at a DC-oﬀset of VDC = 6V and peak-to-peak voltage of Vpp = 3V for increasing modulation frequency (solid). OSA resolution 0.1 nm.

76 CHAPTER 5. VCSEL RESULTS

f = 815 kHz

f = 820 kHz

0 Q = 3

4 4 Q = 3774

3 3

2 2 Displacement [pm] Displacement Displacement [pm] Displacement

1 1

0 0

816 818 820 822 824 400 600 800 1000 1200 1400 1600

Frequency [kHz] Frequency [kHz] (a) (b)

Figure 5.11: Plot of the displacement spectrum of the (a) thermal noise oscillation (b) forced oscillation with vDC = 2V and vAC = 2V.

2.20). Figure 5.11b shows the mechanical spectrum measured with a forced oscillation with an excitation of vDC = 2V and vAC = 2V at atmospheric pressure. The resonance frequency is determined to be 815 kHz and the mechanical Q- factor 3.2. This compares to the dynamic measurements done using an optical spectrum analyzer.

5.3.6 Discussion Characterization of the HCG VCSEL show single-mode operation for current up to thermal roll-over with a minimum of 40 dB SMSR. A 3 dB tuning range of 10 nm has been demonstrated in static mode and more than 20 nm in resonant mode. The resonance frequency of the HCG VCSELs is around 850 kHz which sets the upper limit on the tuning rate. The tuning range is limited by increasing threshold current at the edge of the tuning range. In static operation the HCG VCSEL continues to lase at pull-in. This conﬁrms that the ARC protect the VCSEL from junction breakdown and furthermore shows that high performance HCG VCSELs with oxide gap can be manufactured based on the developed process platform.

77 Chapter 6

Conclusion

The main result of the thesis work has been the establishment of a III-V MOEMS platform for the fabrication of vertical-cavity micro-opto-electro-mechanical systems. This has been used to make Fabry-Pérot filters and tunable VCSELs. For making tunable VCSELs at 1060 nm growth of InAlP sacrificial materials and active gain material has been done. The wet etching properties of InAlP in diluted hydrochloric acid have been examined. The etch rate has been found to be highly anisotropic with the etch- rate being limited by the (111) plane to 0.5µm/min. The selectivity of the etch to other materials has been investigated and it has been found that the etch is selective to GaAs, AlGaAs and Al2O3. For GaAs we show that the selectivity is finite, and much lower that the complete selectivity that is generally stated in literature. The sacrificial material has been used to fabricate monolithic Fabry-Pérot cavities. The Fabry-Pérot filters have been fabricated with a polarization selective top HCG mirror and bottom DBR mirror. The characterization of the filters show that a quality factor of around 200 at 1030 nm is achieved. The gain material, In0.3Ga0.7As/GaAs0.8P0.2 multiple quantum wells has been used to fabricate both standard VCSELs and HCG VCSELs. The gain material shows bright photoluminescence up to 1110 nm, with FWHM down to 20 nm. Gain material with up to 5 quantum wells has been demonstrated. The VCSELs fabricated show single-mode lasing at 1060 nm and are operating up to 60◦C. This, we believe, is the first demonstration of a HCG VCSEL where an air-clad HCG fully replaces the top DBR. The HCG VCSELs show 0.9 mA threshold current and mW output power at room temperature. The full re- placement of the top p-DBR with a HCG will allow optimization of the current spreading layer for better performance in terms of temperature operating range and modulation bandwidth. Static and dynamic tuning is demonstrated for the HCG VCSEL with 1% and 2.1% relative tuning range, respectively. It is demonstrated how resonant tuning can be used to extend the tuning range of the VCSEL. This relax the trade-off between tuning range and tuning rate and will allow widely tunable VCSELs to be operated at MHz frequencies.

78 CHAPTER 6. CONCLUSION

Outlook

Fabry-Pérot filters with a high polarization extinction ratio have applications in implementation where SOAs are used. The polarization selectivity of a Fabry-Pérot filters has been shown using a subwavelength grating. Due to the high index-contrast between the subwavelength grating and the surrounding cladding, the grating provides ultra-high reflectivity. This could enable narrow linewidth filters. Future work should focus on matching the reflectivity of the top HCG mirror to the bottom DBR mirror of the Fabry-Pérot cavity. Measurements with collimated fibers should be done to test the limits to the transmission and linewidth obtainable with such filters. The advantage of VCSELs with highly polarized output is similar to that in Fabry-Pérot filters. The linearly polarized HCG VCSEL will allow higher final power levels to be reached with better stability. The VCSELs are the first fabricated at The Technical University of Denmark for which the epitaxial substrate has been grown in-house. This enables tailoring of the optical properties of the gain material. The wavelength could be blueshifted with the current InGaAs MQW to the 850 nm wavelength which holds several interesting application. Furthermore experiments should be done to redshift the photoluminescense. This could enable 1300 nm VCSEL with improved single-mode output power level at the high modulation speeds used in telecommunication. In all cases continuing the work on VCSEL, the oxidation of the AlGaAs forming the oxide aperture should be further investigated. This both involves experiments with ion implantation and optimization of the growth and wet oxidation of AlGaAs. Further work is needed on the growth of p-doped DBRs to improve the performance of the VCSELs. With further optimization of the free-carrier absorption of the epitaxial design it is believed that the threshold current could be reduced for the DBR VCSEL.

79 Appendix A

Fabry-Pérot Interferometer

In the following the Fabry-Pérot ﬁlter transmission function is derived (see schematic drawing in Fig. 2.7). The incoming light beam, a plane wave

E~ = E exp iωt) zˆ 0 {− } will

1. Experience external reflection at A with a field reflection coefficient r1 and transmission with a transmissioncoefficient t1.

2. The transmitted wave will at B either (a) experience reflection with field reflection coefficient r2 or (b) transmission with transmission coefficient δ t2. The wave will further more have experienced a phaseshift of φ = 2 where δ is the phase difference between succesive transmitted waves.

3. The reflected wave (a) will then at A either (c) experience internal reflection with field reflection coefficient r1 or (d) transmission with transmission coefficient t1.

4. The reﬂected wave (c) will then transmit at B having experienced a further phase shift δ or it will reﬂect looping from the previous step.

The filter is to be used as a transmissive filter and from the above argu- mentation the transmitted wavefront can be written as an infinite sum of the transmitted waves

E = t t E exp iφ + t t r r exp iδ E exp iφ t 1 2 i { } 1 2 1 2 { } i { } +t t (r r )2 exp 2iδ E exp iφ + ... 1 2 1 2 { } i { } = E exp iφ t t + t t r r exp iδ + t t (r r )2 exp 2iδ + ... i { } 1 2 1 2 1 2 { } 1 2 1 2 { } h i = E exp iφ t t 1 + r r exp iδ + (r r exp iδ )2 + ... i { } 1 2 1 2 { } 1 2 { } h 1 i = E exp iφ t t i { } 1 2 1 r r exp iδ − 1 2 { } t t = E exp iφ 1 2 (A.1) i { }1 r r exp iδ − 1 2 { }

80 APPENDIX A. FABRY-PÉROT INTERFEROMETER where subscript 1 and 2 refers to the HCG and DBR mirror respectively. The 1 2 transmission can be found from Eq. (A.1) as the ratio of the transmitted, 2 Et , to the incident intensity, 1 E 2 | | 2 | i| 2 E t t t∗t∗ T = | t| = exp iφ 1 2 exp iφ 1 2 I E 2 { }1 r r exp iδ {− }1 r r exp iδ | i| − 1 2 { } − 1∗ 2∗ {− } t 2 t 2 = | 1| | 2| 1 r r exp iδ r r exp iδ + r 2 r 2 − 1 2 { } − 1∗ 2∗ {− } | 1| || 2| t 2 t 2 = | 1| | 2| 1 r r exp i(δ θ θ ) r r exp i(δ θ θ ) + r 2 r 2 − | 1|| 2| { − 1 − 2 } − | 1|| 2| {− − 1 − 2 } | 1| || 2| t 2 t 2 = | 1| | 2| 1 2 r r cos(δ ) + r 2 r 2 − | 1|| 2| ′ | 1| || 2| t 2 t 2 = | 1| | 2| 1 + 4 r r sin2(δ /2) 2 r r + ( r r )2 | 1|| 2| ′ − | 1|| 2| | 1|| 2| t 2 t 2 = | 1| | 2| (A.2) (1 r r )2 + 4 r r sin2(δ /2) − | 1|| 2| | 1|| 2| ′ where the field reflection coefficient in general is a complex number that can be written as a r = r exp iθ | | {− } where θ will be referred to as the reflection phase (θ [ π; π]). In this nomen- clature the phase difference then includes the Fresnel∈ reflection− phases of the two mirrors δ′ = δ θ θ (A.3) − 1 − 2 with the phase difference between two succesive waves being 4πn g δ = 0 (A.4) λ in case the light is surface normal. Here g is the gap distance, n0 the refractive index of the gap medium and λ the wavelength.

81 Acronyms

ARC anti-reflective coating ARDE aspect-ratio dependent etching ASE Amplified Stimulated Emission CMOS complementary metal-oxide-semiconductor CW Continous Wave DBR Distributed Bragg Reflector DSP Digital Signal Processing ECL External Cavity Laser FDTD Finite-Difference Time-Domain FDML Fourier Domain Mode-Locked FSR Free Spectral Range FWHM Full-Width at Half-Maximum GMR Guided-Mode Resonance GIRO GIant Reflectivity to zero Order HCG High-index Contrast subwavelength Grating ICP Inductively Coupled Plasma laser Light Amplification by Stimulated Emission of Radiation LIV Light-Current-Voltage MM multimode ND Neutral Density maser Microwave Amplification by Stimulated Emission of Radiation MEMS Micro-Electro-Mechanical Systems MOEMS Micro-Opto-Electro-Mechanical Systems MOVPE Metal-Organic Vapour Phase Epitaxy

82 APPENDIX A. FABRY-PÉROT INTERFEROMETER

MQW Multiple Quantum Well

OCT Optical Coherence Tomography

OSA Optical Spectrum Analyzer

PCF photonic crystal ﬁber

PL Photoluminescence

PM Polarization Maintaining

QW Quantum Well

RCLED Resonant-Cavity Light Emitting Diode

RCWA Rigorously Coupled Wave Analysis

RIE Reactive Ion Etching

SD-OCT Spectral-Domain OCT

SGDBR Sampled Grating DBR

SM Single Mode

SOA Semiconductor Optical Ampliﬁer

SS-OCT Swept Source OCT

SMSR Side-Mode Suppression Ratio

TE Transverse Electric

TM Transverse Magnetic

TMM Transmission Matrix Method

VCSEL Vertical-Cavity Surface-Emitting Laser

XRD X-Ray Diﬀraction

ZNS Zero Net Strain

WDM Wavelength Division Multiplexing

Chemical compounds

HSQ hydrogen silsesqouioxane

CBr4 carbon tetrabromide

CHF3 ﬂouroform

CH4 methane TMAl trimethylaluminum

83 APPENDIX A. FABRY-PÉROT INTERFEROMETER

Si2H6 disilane

Si3N4 silicon nitride

SiO2 silicon oxide

PH3 phosphine TBP tributhylphosphine

TMGa trimethylgalium

AsH3 arsine TMIn trimethylindium

BHF buﬀered hydroﬂouric acid

VOC Volatile Organic Compound

84 List of publications

The following is a list of the publications to which the author has contributed that has been published during the duration of the PhD (Nov 2008 – June 2012). Publications marked with / are based on earlier work. Non peer-reviewed articles are markeed with . ∈ † Published

I T. Ansbæk, C. H. Nielsen N. B. Larsen, I. S. Chung, D. Larsson and †K. Yvind. Time-resolved measurement of the light-current characteristic of a coated VCSEL diode in acetone vapour. International Nano- Optoelectronics Workshop, Berlin-Stockholm, 2009.

II T. Ansbæk, C. H. Nielsen, N. B. Larsen, S. Dohn, A. Boisen, I.S. Chung, †D. Larsson and K. Yvind. Acetone vapor sensing using a vertical cavity surface emitting laser diode coated with polystyrene. Annual Conference on Commercialization of Micro and Nano Systems 14, Copenhagen, 2009.

III / T. Ansbæk, D.H. Petersen, O. Hansen, J. B. Larsen, T. M. Hansen P. ∈Bøggild. Fundamental size limitations of micro four-point probes. Micro- electronic Engineering 4-6 (86) pp. 987–990, 2009.

IV / G. Fragiacomo, T. Ansbæk, T. Pedersen, O. Hansen and E. V. Thomsen. ∈Analysis of small deﬂection touch mode behavior in capacitive pressure sensors. Sensors and Actuators A: Physical 1 (161) pp. 114–119, 2010.

V T. Ansbæk, C. H. Nielsen, N. B. Larsen, S. Dohn, A. Boisen, I. S. Chung, †D. Larsson and K. Yvind. Polymer-coated vertical-cavity surface-emitting laser diode vapor sensor. Proceedings of SPIE (7615) pp. 76150A, 2010.

VI / G. Fragiacomo, E. V. Thomsen and T. Ansbæk. Validation of an an- ∈alytical model for contact mode plate deﬂection of touch mode capacitive pressure sensors. Sensing Technology (ICST), 2011 Fifth International Conference on, New Zeeland, pp. 634–638, 2011.

Under preparation

VI T. Ansbæk, C. H. Nielsen, S. Dohn, I.S. Chung, D. Larsson and K. Yvind. Vertical-cavity surface-emitting laser vapor sensor using swelling polymer reﬂection modulation. Accepted for publication in Applied Phys. Lett.

85 APPENDIX A. FABRY-PÉROT INTERFEROMETER

VII T. Ansbæk, E. Semenova, O. Hansen and K. Yvind. Crystallographic dependence of the lateral undercut wet etch rate of Al0.5In0.5P in diluted HCl for III-V sacriﬁcial release. Submitted to J. Vac. Sci. B.

VIII T. Ansbæk, I. S. Chung and K. Yvind. 1060 nm Tunable Monolithic High Index Contrast Subwavelength Grating VCSEL. Submitted to IEEE Pho- ton Tech. Lett.

IX T. Ansbæk, I. S. Chung and K. Yvind. Resonant Tunable Vertical-Cavity Surface-Emitting Laser. To be submitted to Optics Express.

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